Democratic lawmakers want the Securities and Exchange Commission to follow through on suggested improvements to corporate disclosures on board diversity.

Shortly before Mary Jo White stepped down as the SEC’s chairman, she asked the staff to review reporting requirements with an eye toward seeking more details on directors’ diversity. Now Rep. Gregory Meeks (D-N.Y.) and 28 of his peers in the House are calling on the commission’s new chairman to finish the work she started.

“The SEC’s corporate board diversity rule is broken,” Meeks said in a statement May 25. “Although many companies have complied with the spirit of the...