But the president’s legal strategy has been more complicated. His administration announced in 2011 that it would not defend the constitutionality of the key section of the Defense of Marriage Act that excluded gay couples from federal marriage benefits. In a 5-to-4 decision in 2013, the Supreme Court agreed.

At the same time, the administration stopped short of asking the justices to strike down all state prohibitions on same-sex marriage. That is the question the court will decide this term, with oral arguments scheduled for April 28.

The government’s brief this time is unequivocal. It says that restrictions on gay marriage violate the Constitution’s guarantee of equal protection and, for the first time, calls on the court to recognize sexual orientation as a characteristic — like race or gender — that deserves special protection.

“In Loving v. Virginia, this court applied the ‘most rigid scrutiny’ under the Equal Protection Clause to invalidate state laws banning interracial marriage,” said the brief filed by Solicitor General Donald B. Verrilli Jr. “There is similarly no reason to water down the otherwise appropriate level of scrutiny here.”