Still, the move “will have a very significant impact because it is easier for the courts to say ‘we think this law is unconstitutional’ if another branch is already saying that,” said Jon Davidson, the legal director of Lambda Legal, one of the groups that has challenged the law in court.

He pointed to an order issued Thursday by U.S. District Judge Jeffrey White in the Northern District of California in a case about granting health benefits to the gay spouse of a federal worker in California, a state that briefly allowed gay marriage in 2008.

In the order, Judge White asked lawyers defending the U.S. Office of Personnel Management, “How does the Executive [Branch] reconcile the position that it intends to enforce a statute that it has affirmatively declared to be unconstitutional and deemed inappropriate to defend?”

A Department of Justice spokeswoman declined to comment on the case.