Two groups on Tuesday asked the New Mexico Supreme Court to legalize gay marriage in the state.

New Mexico is the only U.S. state that neither recognizes nor prohibits the recognition of the unions of gay and lesbian couples. The New Mexico Constitution's definition of marriage is gender neutral.

However, opponents have cited the state's application for a marriage license, which includes spaces to list the bride and the groom, as reason to not allow gay couples to marry. New Mexico Attorney General Gary King has described the terms as “gender specific.”

In a writ of mandamus filed with the New Mexico Supreme Court, the groups ask the court to clarify whether gay couples can marry in New Mexico.

“The United States Supreme Court's decision to overturn DOMA has increased our sense of urgency to clarify the ability of same-sex couples to marry in New Mexico,” said Peter Simonson, executive director of the New Mexico chapter of the ACLU. “With all barriers to federal recognition removed, our state cannot stand by as thousands of same-sex couples, many of whom were married out of state, continue to be denied those protections.”

The National Center for Lesbian Rights (NCLR) joined ACLU-NM in filing the motion. In March, the groups filed a lawsuit on behalf of several gay couples who wish to marry in New Mexico.

(Related: Gay marriage legal in New Mexico, Santa Fe council says.)