The White House said in a court filing on Monday that Musk's role in the Trump administration was that of a White House employee and senior adviser to the president, and that he had no authority over DOGE and was not an employee of the program.
The White House declared this to a judge in a case filed by Democratic attorneys general against Musk and DOGE.
Trump appeared to contradict at least part of the White House assertion on Wednesday.
"I signed an order creating the Department of Government Efficiency and put a man named Elon Musk in charge," Trump told an audience of investors and company executives in Miami.
The President has repeatedly talked about Musk as the functional leader of DOGE, which is not a cabinet-level department, featuring him in a news conference at the White House this month to answer questions about the program.
Trump on his first day in office set up the cost-cutting body in an executive order that did not say who its "administrator" would be. White House officials this week have not answered repeated requests to identify the administrator.
DOGE has swept through federal agencies since Trump began his second term as president last month. Musk, chief executive of carmaker Tesla, was put in charge of rooting out what the White House calls wasteful spending as part a dramatic overhaul of government that has included thousands of job cuts.
Musk has been accused of a host of conflicts of interest between his business interests and his efforts to cut costs for the federal government. The White House has said the billionaire will recuse himself if any conflicts of interest arise.
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