A top Microsoft Corp. executive is calling for the U.S. government to regulate facial-recognition technology, an area Apple Inc., Alphabet Inc.’s Google, Facebook Inc. and other tech-giant rivals have made significant bets, and where Microsoft has made its own investments.

It is also the latest controversial topic Brad Smith, Microsoft’s president and chief legal officer, has taken on. He has recently challenged the Trump administration over the immigration travel ban and the separation of children from parents at the Mexican...