Nasdaq Inc.’s push for greater diversity in corporate boards faces a key hurdle as regulators are poised to rule on the exchange operator’s proposal to include gender and race in its listing rules.

Staffers at the Securities and Exchange Commission are expected to release a decision Friday on whether to approve or reject Nasdaq’s proposed changes. Under the proposal, Nasdaq-listed companies would need to meet certain minimum targets for the gender and ethnic diversity of their boards or explain in writing why they aren’t doing so.

For most U.S. companies, the target would be to have at least one woman director, as well as a director who self-identifies as a racial minority or as lesbian, gay, bisexual, transgender or queer. Companies would also be required to disclose diversity statistics about their boards. Nasdaq found in a review conducted before submitting its plan late last year that more than three-quarters of its listed companies wouldn’t have met its proposed requirements.

Republicans on the Senate Banking Committee and some conservative groups have criticized the plan, saying Nasdaq is overreaching and pursuing a political agenda. Democrats on Capitol Hill and corporations such as Goldman Sachs Group Inc. and Microsoft Corp. have voiced support for the proposal.

The SEC must sign off on changes to stock exchanges’ listing rules. Nasdaq filed its proposal with the agency in December 2020, setting off a 240-day period for commission staffers to make a decision. That period expires Sunday. In such situations, the SEC typically releases its decision ahead of the weekend.

So far, the agency has been quiet on Nasdaq’s diversity push. SEC Chairman Gary Gensler, an appointee of President Biden, said during a confirmation hearing in March that companies benefit from diversity on their boards. But he didn’t take a stance on Nasdaq’s proposal.

SEC staffers might not have the final word on the plan. Under agency procedures, one of the SEC’s five commissioners can call for a review of the staff’s decision or an outside group can petition for such a review. That would require the commissioners to approve or reject Nasdaq’s diversity proposal in a majority vote, following an additional review that could take months.

Critics of Nasdaq’s plan have warned that it could be challenged in court. Some conservative groups have argued that the exchange’s diversity rule, if implemented, would violate the U.S. Constitution and civil rights laws.

“The proposed rule is racist and sexist in that it mandates that firms establish quotas and discriminate based on sex, skin color, ethnicity or sexual orientation,” David Burton, a senior fellow at the Heritage Foundation, told the SEC in a January letter.

Lawyers for Nasdaq say the rule wouldn’t violate any laws. Nasdaq has rejected characterizations of its proposed rule as a mandatory quota system, since companies would have the option of filing a written explanation for why they weren’t meeting the diversity targets.

The exchange operator also amended its initial proposal to make it easier for small companies to comply. One of the changes, for instance, allows companies that have five or fewer directors to meet the targets with just one board member from a designated diverse background, rather than two.

Nasdaq argued that its proposed rule change would benefit investors. The exchange operator cited studies that found companies with more diverse boards tended to have stronger corporate governance and financial performance.

A variety of Wall Street initiatives have sought to bring more diversity to U.S. corporate boards, which remain heavily white and male.

Asset managers such as BlackRock Inc. and State Street Global Advisers have pushed their portfolio companies to appoint more women as directors. Last year, Goldman said it would no longer underwrite initial public offerings of companies in the U.S. and Europe unless they had at least one “diverse” board member. The bank recently raised that target to two diverse directors.

An analysis released in June found that big U.S. companies significantly boosted the share of new directors who are Black or Latino this year, and have added more women to their boards in recent years.

Nearly 75% of new independent directors at companies in the S&P 500 are women or belong to a racial or ethnic minority, up from about 60% last year and 31% a decade ago, according to the analysis by board and executive recruiting firm Spencer Stuart.

Still, the shift left around 80% of board seats occupied by white directors and about 70% by men. About 11% of S&P 500 board members are Black, 4% are Latino and 6% are Asian, Spencer Stuart found.

—Theo Francis contributed to this article.

Write to Alexander Osipovich at alexander.osipovich@dowjones.com