WASHINGTON (Reuters) - The Obama administration outlined its argument on Friday why the U.S. Supreme Court should strike down a federal law that defines marriage as between a man and woman.

Solicitor General Donald Verrilli filed a brief with the court saying that section 3 of the Defense of Marriage Act was unconstitutional, expanding on the administration's approach to the controversial 1996 law, which it has formally opposed since February 2011.

Section 3 defines marriage under federal law as being between a man and a woman.

The law denies federal benefits to same-sex married couples that are granted to married heterosexuals.

The administration's position is that the law violates the guarantee of equal protection under the law.

In the brief, Verrilli said there was a history of discrimination against gays and lesbians that required the Supreme Court to take a careful look at any law that specifically targets them as a group.

He therefore urged the court to take an approach to analyzing the law known as "heightened scrutiny," which, if adopted by the court, could make it more likely the court would find the law unconstitutional.

"The law denies to tens of thousands of same-sex couples who are legally married under state law an array of important federal benefits that are available to legally married opposite sex couples," he wrote.

The Supreme Court is set to hear arguments in the case on March 27, the day after it weighs the constitutionality of a California law, Proposition 8, which banned gay marriage in that state.

The administration has until Thursday to decide whether to weigh in on Proposition 8.

(Reporting by Lawrence Hurley; Editing by Kevin Drawbaugh and Peter Cooney)