A simmering dispute between the Department of Government Efficiency and an independent agency dedicated to promoting peace broke into an open standoff involving the police on Monday, as Elon Musk’s government cutters marched into the agency’s headquarters and evicted its officials.

The dramatic scene played out in Washington on Monday afternoon as Mr. Musk’s team was rebuffed from the U.S. Institute of Peace, an agency that President Trump has ordered dismantled, then entered it with law enforcement officers. Agency officials say that because the institute is a congressionally chartered nonprofit that is not part of the executive branch, Mr. Trump and Mr. Musk do not have the authority to gut its operations.

“DOGE just came into the building — they’re inside the building — they’re bringing the F.B.I. and brought a bunch of D.C. police,” Sophia Lin, a lawyer for the institute, said by telephone as she and other officials were being escorted out.

George Moose, who was fired as the institute’s acting president last week but is challenging his dismissal, accused Mr. Musk’s team of breaking in. “Our statute is very clear about the status of this building and this institute,” he told reporters. “So what has happened here today is an illegal takeover by elements of the executive branch of a private nonprofit corporation.”

The standoff quickly became one of the most visible points of resistance to Mr. Musk’s effort to fire federal workers and dismantle whole agencies. And it underscored Mr. Trump’s willingness to push the legal limits of his authority in his drive to reshape the federal government and put even entities that have traditionally been independent under his thumb.