Lawyers representing House Republicans and the Obama administration on Friday each claimed the other cannot participate in a lawsuit before the Supreme Court challenging the Defense of Marriage Act (DOMA).

The Bipartisan Legal Advisory Group (BLAG), under the direction of House Speaker John Boehner, a Republican from Ohio, filed a legal brief in the case, known as Windsor v. United States, arguing that the Justice Department lacks the legal standing to participate in the lawsuit because it received the outcome it sought in lower courts.

“It obtained the precise relief it believed was appropriate based on the precise theory [heightened scrutiny] it advocated,” BLAG lawyers wrote. “The executive can fare no better before this Court. While this Court's affirmance would have a greater precedential impact, the executive cannot ground its appellate standing on a desire for an opinion with the identical effect on this case and controversy, but a broader precedential scope for other cases.”

After the Justice Department announced in 2011 that it would no longer defend the law in court, Boehner directed BLAG to step in. BLAG hired former Solicitor General Paul Clement to argue more than a dozen cases challenging the constitutionality of DOMA, which bans federal agencies from recognizing the legal marriages of gay and lesbian couples.

In a brief addressing jurisdictional questions in the case, the Justice Department argued that BLAG lacks standing in the case.

“BLAG is an entity located within the Legislative Branch,” DOJ lawyers wrote. “The Constitution assigns to that Branch only specifically enumerated 'legislative powers.' … Although Congress (and the individual Houses) may create offices to assist with legislative tasks, the authority of such an office may not include the 'discretionary power to seek judicial relief' on behalf of the United States.”

In a separate brief also filed on Friday, the administration argued that DOMA is unconstitutional and should be struck down.