Three Democratic senators asked a Federal District Court judge on Monday to issue an injunction barring Matthew G. Whitaker from exercising the powers of head of the Justice Department, arguing that President Trump’s installation of Mr. Whitaker as acting attorney general violated the Constitution.

The senators — Richard Blumenthal of Connecticut, Mazie K. Hirono of Hawaii and Sheldon Whitehouse of Rhode Island — sit on the Judiciary Committee, which conducts confirmation hearings for attorney general nominees. They argued that an official who had not been Senate-confirmed could not run the Justice Department, even temporarily.

“Because the Senate has not consented to Mr. Whitaker serving as an officer of the United States, his designation by the president to perform the functions and duties of the attorney general violates the Appointments Clause” of the Constitution, the complaint said. “If allowed to stand, Mr. Whitaker’s appointment would create a road map for the evasion of the constitutionally prescribed Senate advice-and-consent role.”

The lawsuit is the latest effort by critics of Mr. Trump’s move, which followed his ousting of Attorney General Jeff Sessions this month, to temporarily install Mr. Whitaker in his place as the nation’s top law-enforcement official. Without control of either chamber of Congress — they will take over the House of Representatives in January — Democrats have few other tools to apply pressure for now.

Mr. Whitaker, whom the White House previously installed as Mr. Sessions’s chief of staff, is widely seen as a Trump loyalist. His powers now include supervising Robert S. Mueller III, the special counsel running the investigation into whether Mr. Trump’s associates conspired with Russia when it interfered in the 2016 election. Mr. Whitaker has been an outspoken critic of that investigation. He has separately come under scrutiny for his role with a company that a federal judge shut down for defrauding its customers.

In an interview with Fox News that aired on Sunday, Mr. Trump claimed that he did not know that Mr. Whitaker had criticized the Russia investigation before he designated him acting attorney general, circumventing Deputy Attorney General Rod J. Rosenstein. Mr. Trump also said he would not stop Mr. Whitaker if he decided to limit or curtail the investigation.

Last week, litigants in at least two pending, unrelated lawsuits against Mr. Sessions in his official capacity submitted motions asking judges to declare that by law, Mr. Rosenstein should be his rightful acting successor and so his name, not Mr. Whitaker’s, should be substituted as the defendant in the litigation. One such motion was filed in the Federal District Court for the District of Maryland, and the other in the Supreme Court.

The new lawsuit, filed in the Federal District Court for the District of Columbia, was brought on behalf of the senators by two watchdog groups, Protect Democracy and the Constitutional Accountability Center. They maintained that the lawmakers had legal standing because their constitutional authority to cast confirmation votes for senior government officials had been nullified.

“If the practice undertaken in this matter is upheld, it creates a road map for deliberately going around the constitutional requirement for advice and consent,” Mr. Whitehouse said in an interview.

The case was assigned to Judge Trevor N. McFadden, a Trump appointee.

The Justice Department last week disclosed an Office of Legal Counsel memo arguing that Mr. Whitaker’s temporary appointment was lawful under the Vacancies Reform Act of 1998. It also cited an 1898 Supreme Court opinion and numerous historical examples in support of the proposition that an office whose holder must normally be Senate-confirmed can be temporarily filled by an acting official who has not gone through the confirmation process.

“There are over 160 instances in American history in which non-Senate-confirmed persons performed, on a temporary basis, the duties of a Senate-confirmed position,” Kerri Kupec, a Justice Department spokeswoman, said in a statement on Monday. “To suggest otherwise is to ignore centuries of practice and precedent.”

The Justice Department memo pointed to various examples of such a temporary appointment dating back to the earliest days of American history, although it acknowledged that there was very little precedent for an acting attorney general who did not undergo confirmation. There was such an acting attorney general in 1866 for several days, but that was before Congress had created a Justice Department for that official to supervise.

In an interview, Mr. Blumenthal said that most of the historical examples the administration had cited involved short-term appointments demanding immediate attention whose constitutional legitimacy was never tested in court. He also argued that the attorney general’s special powers set that office apart.

“In modern times, this kind of appointment is unprecedented, certainly for an office of this importance,” he said.

In the House, where Democrats will assume control in January, they may soon have more leverage. Representative Jerrold Nadler of New York, the incoming chairman of the Judiciary Committee, has pledged to make Mr. Whitaker his first hearing witness and to subpoena him if necessary. He has warned that there would be consequences for firing Mr. Mueller.

And in a series of letters, Mr. Nadler and other soon-to-be Democratic chairman have put the Justice Department and the White House on notice that they intend to investigate the circumstances of Mr. Sessions’s removal and replacement, and will request access to communications related to both.

But the warnings highlight the dilemma for lawmakers worried that Mr. Trump or his associates might act to curtail the inquiry. Even though Democrats can use the House majority to try to check those impulses, they have no real say over presidential appointments — and in any case, it will be several more weeks until they actually gain access to the levers of power.