In the ongoing battle over Elon Musk’s role in the Trump administration, the Department of Justice has weighed in with new analogies, saying he exercises the same sort of power that first lady Hillary Clinton did for her husband or political strategist Karl Rove did for President George W. Bush.

In other words, government lawyers said, he’s an important voice for President Trump, but it’s only by dint of his ideas and personality.

He holds no formal power to act as an officer of the U.S., the lawyers said in a new filing Friday with a federal judge.

“The White House has long been populated by aides and advisors who wield tremendous de facto sway over government. Hillary Clinton was charged with reforming the nation’s healthcare system; Karl Rove designed much of the Bush Administration’s domestic policy,” Joshua E. Gardner, special counsel at the Justice Department, said in a brief.

Mr. Gardner said Mr. Trump may choose to receive advice from Mr. Musk, but it is the president — and other officers appointed under the Constitution — who actually exercise executive powers.

Mr. Musk has become a gargantuan figure in Trump 2.0, drawing perhaps even more ire than Mr. Trump from Democrats and others upset at the president’s aggressive agenda.

The administration insists Mr. Musk is not secretly wielding powers on behalf of the president.

Indeed, the Justice Department has argued that the world’s richest man, at least for purposes of government, is nothing more than a senior adviser to the president.

He isn’t even even part of the Department of Government Efficiency and “has no actual or formal authority to make government decisions himself,” Joshua Fisher, head of the White House administration office, said in a court declaration last month.

Mr. Trump, however, continues to undercut those statements.

“I have created the brand new Department of Government Efficiency, DOGE. Perhaps you’ve heard of it. Perhaps. Which is headed by Elon Musk, who is in the gallery tonight,” Mr. Trump said in his address to Congress earlier this month.

A day after the speech, states challenging Mr. Trump rushed to share that statement with U.S. District Judge Tanya S. Chutkan.

Two days later, on Friday, the Justice Department reiterated its position that Mr. Musk is a “special government employee” who does not occupy an “office” of the U.S. government.

The states, led by New Mexico, argued that Mr. Musk is still wielding de facto power and said that violates the Constitution’s Appointments Clause.

The Justice Department said that for the purposes of the legal debate, de facto power doesn’t matter.

“The Appointments Clause is concerned with the formal powers vested in an office by law, not an individual’s perceived informal influence,” Mr. Gardner said.

Otherwise, he said, an effective White House chief of staff whose opinion is followed would be considered an officer while an ineffective one whose opinion was ignored would not be.