Is there a total stock market index fund in India, like the one offered by Vanguard in the US?

There are two primary indices in India, the NIFTY 50 and SENSEX (30).

There are many funds that invest in either of these indexes. While these may not be representative of the entire stock market, they would represent a significant percentage. Most total stock market funds are capitalization weighted, so proportionately invest more in the larger market cap companies.

The problem with investing in broader less popular indices is that they may be less liquid and their constituents may be less liquid, resulting in higher transaction costs that will reduce gains.

An important factor also when choosing funds is the expense ratio. Higher expense ratios can make a significant difference over years of holding the positions.

I'm a fan of Jhon Bogle and his follower JL Collins and their investment philosophy and most importantly, investor of VTSAX fund. To answer your question, I feel Nifty 500 Index Fund comes very close to VTSAX. It's offered by Motilal Oswal.

Also, let me know if you found anything better than this.

Not a complete market index but you can checkout NIFTYBEES & JUNIORBEES. Both are Exchange Traded Funds. The Niftybees tracks the NIFTY index i.e. the top 50 companies & the Juniorbees tracks the next 50. So with a combination of these two, you can invest in top 100 companies on NIFTY.