Democratic legislation to make publicly traded companies report on the diversity of their boards and executive management teams has gotten endorsements from both institutional investors and a leading business lobby.

The U.S. Chamber of Commerce and the Council of Institutional Investors have endorsed the legislation reintroduced Feb. 6 by Rep. Gregory Meeks (D-N.Y.). Neither group took a position on an earlier version of Meeks’ bill from 2017.

Institutional investors have so far led the push to diversify company leadership by...