Could a president sue a person for defamation during their time in office?

In this hypothetical (unless it’s happened in the past), a prominent citizen or news agency makes statements about the president, or his decisions or policies, that are knowingly inaccurate or false while he is in office. In the opinion of the president and his counsel in this hypothetical, these false statements harm his reputation or otherwise cause damages to him or his administration.

Given that there are always people who openly criticize a president’s decisions, to varying degrees of accuracy or hyperbole, would the president ever have the option of bringing charges against said person(s), this situation?

Are there laws specific to the executive branch in this case, or for government officers in general?

Note: I’m not referring to any president in particular, and don’t wish for this to become a political debate.