President Trump on Monday fired the three Democratic-selected members of an independent civil liberties watchdog agency, leaving it paralyzed as Mr. Trump’s administration starts to put its stamp on the F.B.I. and intelligence community.

Last week, the day after Mr. Trump’s inauguration, Trent Morse, the deputy director of presidential personnel, sent emails to the agency, the Privacy and Civil Liberties Oversight Board, ordering the three members — Sharon Bradford Franklin, Edward W. Felten and Travis LeBlanc — to submit their resignations by that deadline, saying Mr. Trump would terminate them if they did not.

But the deadline came and went. Having received no further word, the three remained in their positions on Friday, when the board released a long-in-the-works study of terrorism watchlists, which keep people off planes or subject them to extra screening at airports.

On Monday afternoon, however, Mr. Morse sent emails to the three members of the board informing them of their dismissals. The New York Times reviewed one of the emails, and Ms. Franklin and Mr. LeBlanc confirmed that all three had been fired.

Mr. Trump did not remove the sole Republican-selected member, Beth Williams, and a fifth seat was already vacant.

But the agency needs at least three members to take official actions like starting a new investigative project or issuing a board report with a policy recommendation, so the move has crippled its ability to function.

Mr. Trump would have been able to appoint a Republican majority even without the firings. Mr. Felten had been set to stay on until as late as January 2026, and Mr. LeBlanc till January 2029. But the tenure of Ms. Franklin, the board’s chairwoman, was about to end.

In a statement, Ms. Franklin called the firings unnecessary, while also expressing regret that the board would be unable to issue a planned report on a data privacy agreement between the European Union and the United States.

“This isn’t about me — my term was set to end later this week anyway,” she said. “But I am devastated by the attack on the board’s independence and the fact that our agency will have too few members to issue official reports.”

Congress established the agency as an independent unit in the executive branch after the Sept. 11 terrorist attacks to investigate national security activities that can intrude upon individual rights, like the government’s use of surveillance affecting Americans.

It has security clearances and subpoena power, and is set up to have five members, appointed by the president and confirmed by the Senate, who serve six-year terms and can stay on for another after that if no successor has been confirmed. Some members are picked by the president, and some are selected by congressional leaders of the other party.

In a statement, Mr. LeBlanc thanked Mr. Trump for having appointed him in his first term, after Democrats selected him, but said that cutting short the terms Congress had intended the Democratic members to serve would undermine the board’s independence in performing oversight work that is “absolutely essential to accountability in a democracy.”

“I regret that the board’s partisan shift will ultimately undermine not only the mission of the agency, but public trust and confidence in the ability of the government to honor privacy rights, respect civil liberties, honestly inform the public, and follow the law,” Mr. LeBlanc said.