As Estonia is close to Finland, most time of the Soviet occupation was in Estonian Radio a department of Finnish broadcast. It started in 1947 (actually March 14th 1947, according to the chronicle of Estonian broadcasting, in Estonian, on the webpage of Estonian Broadcasting Museum) as Soviet propaganda channel and shifted to Estonian info channel during Singing revolution.

From introduction of thesis of Albert Ludwig Roine:

Vähetuntud on fakt, et Eestit kui piiriäärset Nõukogude vabariiki kasutati kommunistliku propaganda levitamiseks Soomes. Sihtriigis suurema efektiivsuse saavutamiseks tehti propagandasaateid soome keeles. Eesti Raadio regulaarsetest soomekeelsetest saadetest esimene anti eetrisse 14. märtsil 1947 ning nendega jätkati igapäevaselt kuni viimase saateni 28.06.1998.

Google translate gave pretty descent translation:

It is little known that Estonia, as a border Soviet republic, was used to spread communist propaganda in Finland. In order to be more effective in the destination country, propaganda programs were broadcast in Finnish. The first of Eesti Raadio's regular Finnish-language programs was broadcast on March 14, 1947, and they continued daily until the last program on June 28, 1998.

@LangLangC's answer mentioned

This gets even more interesting when one would look at the propaganda against each each other between Soviet Union and China

but did not go into details.

There is evidence suggesting that in the early 1980s until 1989, Chinese authorities prioritised jamming Soviet, Vietnamese and Taiwanese radio stations over Western radio stations.

For example, the following Chinese propaganda bookmark titled 严禁收听敌台反动广播(Prohibition on Listening to Reactive Broadcasting by Enemy Stations) claims

苏越蒋电台 (Radio stations based in the USSR, Vietnam and Taiwan)

对我怀敌意 (Are driven by hostile intent)

造谣和欺骗 (Through rumours and deception)

唆使你犯罪 (They point to a road of crime)

The following leaflet distributed by Taoyuan County, Hunan Province, states:

一、苏联、越南、台湾当局的反动广播电台是敌台，严禁收听 (I. Reactionary radio stations operated by Soviet, Vietnamese and Taiwanese authorities are enemy radio stations; listening is strictly prohibited)

...

三、按照敌台广播的通讯地址向敌特机关写信挂钩，是反革命行为 (III. Writing to addresses given by enemy stations is counterrevolutionary behaviour)

Mentions of western stations are conspicuously rare in artifacts of that period.

Question:
Did the Soviet Union or its satellite states have any broadcast propaganda media for an international audience?

The official international radio service for the Soviet Union was Radio Moscow, or Radio Moscow International Broadcast Service. Its first broadcast was in 1923 in German. By 1931 it operated under 8 languages, By 1970 it broadcast in 64 languages. It was a global radio service which operated across Russia, Europe, eventually during the cold war its service was extended to Africa and North America.

It operated until 1993 when it was reorganized into Voice of Russia.

Let me add to the previous answer some Soviet media outlets.

Soviet Union, a journal published in 18 languages.

It had a supplement called "Sports in the USSR".

Moscow news - a newspaper published in English, and several other languages. (In 1970s this was the only periodical in English available to most Soviet citizens, so students read it to practice their English:-)

There was also a a whole publishing house called Progress which published many books in many languages, mostly for export, mostly translated from the Russian, and works of Marx and Engels.

Yes. Ample supply. At least for print and radio.

Newspapers and magazines

Not really 'broadcast medium', but mentioned in the question:

Many versions printed directly under the auspices of a communist party, and openly sold as such. Example the Peking Review.

^{— West-German National football (soccer) team player Paul Breitner, Maoist at the time, reading the German version of Peking Rundschau (printed since 1964) in 1973. src: Layth Yousif: "Breitner: Rebel Without a Cause", In Bed with Maradona, 2013.}

Western communist parties funded by eastern counterparts with their own newspapers. Example the German Communist Party DKP from 1968, at first a creation most closely tied to the Socialist Unity Party of East Germany. They publish the paper Our Time (Unsere Zeit).
While the direct connection and level of influence for the Soviet Communist Party on the Communist Party of the USA may be somewhat debatable over the course of time, it was for quite some time not to be ignored. Then this list gets really long: English-language press of the Communist Party USA.

Then there were almost 'clandestine' publications. Officially 'unaffiliated' papers with not only a strong 'tendency', but a financial backing from eastern coffers that 'ensured a certain world view' presented to their readers and often allowed circulation in the first place. Example: Studentenkurier of 1955, later renamed konkret.

Television

For large parts of Germany the Eastern TV-stations were also the direct counterpart of the Western TV stations. But while that was a two-way propaganda effort, the limits of the language and the reach of the transmitters held the geographical area covered rather small.

Technological limitations for TV at the time means that likely at most such broadcasts like the 1980 Moscow Olympics might be added to this short list. Although, the propaganda value of such sport events might be judged much lesser than soap operas or 'coloured news' and commentaries.

The most obvious example for this coloured commentary and slanted if not blatant propaganda would be Karl-Eduard von Schnitzler's Der schwarze Kanal,

aimed as well at the eastern home population as well as western viewers tuning in to watch popular movies scheduled before this educational segment in 'improving class consciousness' while using only imperialist (West) German film material, but 'providing politically correct context' via voice over, explanation and commentary.

Fascinatingly, for a quite similar situation compared to Germany, in North Korea, classical radio, which is apparently 'too multipurpose', has had an international outlet from the 1950s onward. But within the state itself radios were very rarely found outside of the possession of the military and political elite. Indeed they are still much rarer than television sets!
But it seems improbable that the few North Korean programmes from 1960s and 1970s forward (basically just Korean Central Television) could have had much impact onto the very diverse scene of South Korean TV, whether for physical or political reach or content attraction.
(Cf. Daniel Schwekendiek: "A Socioeconomic History of North Korea", McFarland, 2014. p74–80)

While there seems to be a scarcity of measurements for the popularity of North Korean TV in the South, this parameter could be gauged for the East/West TV situation in Germany in terms of even western private cable networks offering a feed of DDR1 and DDR2 stations and TV sets being advertised during the 1980s as being capable of not only receiving East German TV, but in colour, too.
_{(as the West used PAL and the East SECAM systems for that. In fact that advertising was just a by-product of East Germany adopting the French system and producers simply built some sets displaying both natively.)}

A certain backfire effect could be observed for the Soviet satellite of the CSSR: The Czechoslovakian TV cooperated for some time in the sixties with the Austrian state TV ORF to broadcast uncensored live talks between East and West. Later then: Similar to Hungarian radio broadcasts during the earlier uprising there, Western people could listen in to cries for help from these Czech communist approved moderators when the Soviets stormed the station during the end of the Prague Spring.

Radio

In terms of radio broadcasters, the earliest and biggest example might be:

Radio Moscow

Type Radio network Country Soviet Union Availability International Launch date 29 October 1929 Dissolved 1993 Replaced by Voice of Russia

Radio Moscow (Russian: Pадио Москва, tr. Radio Moskva), also known as Radio Moscow World Service, was the official international broadcasting station of the Union of Soviet Socialist Republics until 1993. It was reorganized with a new name: Voice of Russia, which has also since been reorganized and renamed Radio Sputnik.
At its peak, Radio Moscow broadcast in over 70 languages using transmitters in the Soviet Union, Eastern Europe, and Cuba.

Non-socialists in the West interested about 'life in the GDR' were from 1959 on directed to tune in to Radio Berlin International.

A list of some other stations from the 'Eastern bloc' to be found at Eastern Bloc media and propaganda Notable Electronic Media in the Eastern Bloc. Also relevant: Radio propaganda – Cold War.

As 'China' went its own ways, Radio Peking (now China Radio International) went on air in 1941. This gets even more interesting when one would look at the propaganda against each each other between Soviet Union and China:
— Sören Urbansky: "The Unfathomable Foe. Constructing the Enemy in the Sino-Soviet Borderlands, ca. 1969–1982", Journal of Modern European History 10(2), p255–278, May 2012. (DOI)

Not really a 'Soviet satellite' either, but Voice of Korea is presenting Juche to the world since 1945 (also in English since 1951) and Pyŏngyang Pangsong sends its Korean language message into the world since 1955.

For Cuba the most important example would be

Radio Havana Cuba (Spanish: Radio Habana Cuba, RHC) is the official government-run international broadcasting station of Cuba.
Although RHC was officially inaugurated in May 1961, the idea of an international Cuban radio station was born in the Sierra Maestra mountains during the final stage of the fight against Fulgencio Batista. After the creation of Radio Rebelde by Ernesto 'Che' Guevara in February 1958, the leadership of the guerrilla movement began to analyze the possibility of creating a radio station after achieving final victory. This station would be able to communicate news about the Cuban Revolution to countries around the world.

During the Cold War, RHC relayed propaganda broadcasts from North Vietnam and North Korea, and the USSR, as well as its original programming. The North Vietnamese programming from the Voice of Vietnam was received by teleprinter and read by Radio Havana Cuba announcers. In the 1960s, Radio Havana Cuba broadcast Radio Free Dixie aimed at African-Americans struggling against segregation and Jim Crow in the southern United States.

In short, when a medium is 'broadcast', it is always 'propaganda', or presenting one side of the stories: 'a world view'. Hence every station using long range frequencies like short wave would qualify for this. (Cf Debra L. Merskin (Eds): "The SAGE International Encyclopedia of Mass Media and Society", Sage, 2019. example)

The interpretation of "falsehood" should also be examined. The interaction between the two principal power blocs is often based on non-interacting value judgments. The propaganda themes on both sides are almost identical, i.e., peace, independence, economic development, racial equality, and cultural freedom; but the interpretations are diametrically opposed. […]

The most interesting developments have, however, taken place in the field of radio. This is where the mixture of subtlety and bluntness appears to be most blatant. During the two-year period of 1967/69, Radio Moscow began transmitting in four new Indian India languages, Assamese, Gujarati, Kannada, and Oriya. By the end of 1969, it broadcast seven hours a week in each of these languages.
Another channel of communication that utilizes Radio Moscow’s technical facilities is called Radio Peace and Progress, and its tone is more belligerent, its thrust more pointed, its message much more inflammatory, than that o fRadio Moscow itself. Yet, the Soviet government disclaims any responsibility for the station. It is, according to the official explanation, an "unofficial, independent radio station." Its concentrated efforts to influence Indian elections and to attack Indian public figures have earned for the station official and unofficial irritation.
_{— Zygmunt Nagorski: "International Propaganda: Its Role, Effectiveness, and Future", The Annals of the American Academy of Political and Social Science, 1971. DOI}

For the general outlook:

Cold War Era The Cold War led to increased international broadcasting (and jamming), as Communist and non-Communist states attempted to influence each other's domestic population. Some of the most prominent Western broadcasters were the Voice of America, the BBC World Service, and the Radio Free Europe/Radio Liberty. The Soviet Union's most prominent service was Radio Moscow and China used Radio Peking (then Radio Beijing, now China Radio International). In addition to the U.S.-Soviet cold war, the Chinese-Russian border dispute led to an increase of the numbers of transmitters aimed at the two nations, and the development of new techniques such as playing tapes backwards for reel-to-reel recorders.

West Germany resumed regular shortwave broadcasts using Deutsche Welle on May 3, 1953. Its Julich transmitter site began operation in 1956, with eleven 100-kW Telefunken transmitters. The Wertachtal site was authorized in 1972 and began with four 500-kW transmitters. By 1989, there were 15 transmitters, four of which relayed the Voice of America.35 Meanwhile, in East Germany, the Nauen site began transmitting Radio DDR, later Radio Berlin International, on October 15, 1959.

In addition to these states, international broadcast services grew in Europe and the Middle East. Under the presidency of Gamal Nasser, Egyptian transmitters covered the Arab world; Israel's service, Kol Yisrael, served both to present the Israeli point of view to the world and to serve the Jewish diaspora, particularly behind the Iron Curtain.

Radio RSA, as part of the South African Broadcasting Corporation, was established in 1966 to promote the image of South Africa internationally and reduce criticism of apartheid. It continued in 1992, when the post-apartheid government renamed it Channel Africa.

Ironically, the isolationist Albania under Enver Hoxha, virtually a hermit kingdom, became one of the most prolific international broadcasters during the latter decades of the Cold War, with Radio Tirana one of the top five broadcasters in terms of hours of programming produced.

From the frontlines back then:

This does not mean, however, that there has been no vigorous action on the part of the Communist broadcasting organizations; but their overall task is much more difficult than that of their Western counterparts, for they not only have to produce their own broadcasts but must also try to keep out the many voices of the opposing camp. The Western broadcasting organizations, on the other hand, are not concerned with silencing the other side and are therefore free to concentrate on putting their material on the air and getting it across to their audience. […]

Almost all European countries, with the refreshing exception of Portugal, have their foreign language services, and additional broadcasts pour in from the other side of the Atlantic and even from the Pacific area. Quite a number of broadcasting organizations in Europe, particularly in Scandinavia, concentrate on the purely informative side by permitting a number of straightforward news bulletins to speak for themselves. The majority of European countries, however, presumably find it useful to augment 'the plain unvarnished truth', as represented by ordinary news bulletins, with a large amount of comment and interpretation.

The Far East, where the cold war has been hotted up in recent years, is a comparative backwater of the radio war, largely because of the small number of receivers available to the population. This does not prevent Asian countries from adding their voices to the universal hubbub. The wars in Korea and Indo-China have, as was only to be expected, pitted the combatant sides against one another over the air as well as in actual battle. Radio Peking, which keeps up a round-the-clock service for South-East Asia, particularly for Chinese residents abroad, also broadcasts in English for listeners in Europe. The Indian and Pakistani broadcasting services have their own antagonism over Kashmir to project, but both find time to broadcast informative bulletins in English and other European languages for audiences in Europe. The Chinese Nationalists on Formosa have a powerful transmitter at their disposal which enables them to provide a day-long listening alternative to Radio Peking's home service.
_{— J. A.: "Radio in the Cold War", The World Today, Vol. 10, No. 6 (Jun., 1954), pp. 245–254.}

Further reading:

— Frederick Charles Barghoorn; "Soviet Foreign Propaganda", Princeton University Press, 1964.
— Gary D. Rawnsley: "Cold-War Propaganda in the 1950s", Macmillan: Basingstoke, 1999.
— Keith Somerville: "Radio Propaganda and the Broadcasting of Hatred: Historical Development and Definitions", Palgrave Macmillan: Basingstoke, 2012.
— Mark Connelly, Jo Fox, Ulf Schmidt & Stefan Goebel (eds.): "Propaganda and Conflict: War, Media and Shaping the Twentieth Century", International Library of Twentieth Century History, Bloomsbury Academic, 2019.