SANTA FE, N.M. — New Mexico’s highest court has asked the state Attorney General and the Santa Fe County clerk to respond to a lawsuit seeking to legalize same-sex marriage.

The state Supreme Court on Tuesday said their legal arguments in the case should be submitted by July 22. No hearing has been scheduled.

The plaintiffs in the case, Alexander Hanna and Yon Hudson of Santa Fe, asked the Supreme Court to order Santa Fe County clerk Geraldine Salazar to issue them a marriage license.

The lawsuit contends that denying marriage licenses to same-sex couples violates the New Mexico Constitution, including its Equal Rights Amendment prohibiting gender-based discrimination.

New Mexico’s laws do not define marriage as between a man and a woman, the definitions are gender-neutral; a statutory list of prohibited marriages also does not list same-sex couples, according to the lawsuit.

Attorney General Gary King’s office said in a non-binding legal analysis last month that gay marriage isn’t allowed in New Mexico but the statutory prohibition may violate the constitution’s equal protection clause.

If the court decides the case, it could resolve a politically difficult issue that has stalled in the Legislature. A proposed constitutional amendment to legalize gay marriage died in the Democratic-controlled Legislature earlier this year.

Associated Press contributed to this report.