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 increasingly voting against directors on boards without any women. The Chamber, Washington’s top business lobby, previously gave its backing to...