President Trump fired FBI Director James B. Comey on Tuesday, saying the country’s top law enforcement agency had lost the public’s trust, but sparked a new round of questions over why he ousted the man leading an investigation into his campaign operatives’ ties to Russia.

Democrats called the firing outrageous, made Watergate comparisons, said it tainted the presidency and insisted the only way forward would be to turn over the bureau’s Russia probe to an independent prosecutor to free it of Mr. Trump’s influence.

Even many Republicans said they were troubled by the firing and praised Mr. Comey for ably handling a tough job. They said his ouster now will only feed perceptions that Mr. Trump is trying to scuttle the investigation.

Mr. Trump insisted he is not personally a target of the probe but said in his dismissal letter to Mr. Comey that he felt compelled to fire him anyway.

“While I greatly appreciate you informing me, on three separate occasions, that I am not under investigation, I nevertheless concur with the judgment of the Department of Justice that you are not able to effectively lead the bureau,” Mr. Trump said.

Mr. Trump has racked up a long list of casualties at the Justice Department: an acting attorney general fired just days into his tenure, the forced resignation of nearly every U.S. attorney and now the head of the country’s premier law enforcement agency.

He said he was acting on the advice of both Attorney General Jeff Sessions and Deputy Attorney General Rod Rosenstein, who both recommended Mr. Comey’s tenure be cut short, with the latter citing his handling of the Hillary Clinton email server investigation.

The White House said the search for a replacement will begin immediately. In the meantime, Mr. Sessions said, Deputy Director Andrew McCabe will act as director.

Whomever the president picks, however, Democrats said that person will be tainted by Mr. Trump’s handling of the situation.

“There can be no question that a fully independent special counsel must be appointed to lead this investigation. At this point, no one in Trump’s chain of command can be trusted to carry out an impartial investigation,” said Sen. Ron Wyden, Oregon Democrat.

Mr. Wyden said he has been a longtime critic of Mr. Comey but called the firing outrageous. He said Congress needs to immediately call a hearing and have Mr. Comey detail his progress in the Trump campaign probe so the public knows where things stand.

Sen. Tim Kaine, Virginia Republican and Mrs. Clinton’s vice presidential running mate, called the firing “the Tuesday night massacre,” harking back to President Nixon’s “Saturday Night Massacre” ouster of the attorney general, the deputy attorney general and the special prosecutor investigating Watergate.

Mr. Kaine, who spoke with The Washington Times while walking alone down a street several blocks from the Capitol hours after the Comey firing, offered no other comment.

Mr. Comey became a major figure in last year’s election, first pursuing an investigation into Mrs. Clinton, then clearing her of criminal wrongdoing over the summer. He inserted himself into the final weeks of the campaign by reopening — then quickly re-closing — the investigation over the finding of more emails.

More recently, he confirmed that the FBI is investigating Trump campaign associates for suspected illegal links to Russia.

Mr. Comey had served as deputy attorney general under President George W. Bush, then was appointed FBI director by President Obama. His term was slated to last through 2023.

In letters Tuesday, Mr. Sessions and Mr. Rosenstein said Mr. Comey had lost their backing.

Mr. Rosenstein blamed the handling of the Clinton probe.

“I cannot defend the director’s handling of the conclusion of the investigation of Secretary Clinton’s emails, and I do not understand his refusal to accept the nearly universal judgment that he was mistaken,” Mr. Rosenstein wrote in a memo to Mr. Sessions. “Almost everyone agrees that the director [made] serious mistakes; it is one of the few issues that unites people of diverse perspectives.”

Mr. Rosenstein said Mr. Comey was “wrong to usurp” Attorney General Loretta E. Lynch’s authority when he took it upon himself to hold a press conference in July to announce that the FBI would not recommend criminal charges against Mrs. Clinton.

The FBI director testified before Congress last week that he took the unusual step because he believed that a June 2016 airport tarmac meeting between Ms. Lynch and former President Bill Clinton had undermined the Justice Department’s credibility to independently investigate the case.

“A number of things had gone on, which I can’t talk about yet, that made me worry that the department leadership could not credibly complete the investigation and decline prosecution without grievous damage to the American people’s confidence in the justice system,” Mr. Comey told senators.

Mr. Sessions wrote in his memo that “a fresh start” was needed in order for the Justice Department to “reaffirm its commitment to long-standing principles that ensure the integrity and fairness of federal investigations and prosecutions.”

Critics said Mr. Sessions, who recused himself from overseeing the FBI’s Russia probe, shouldn’t have played a role in firing the man leading it — though the administration said he was fired for other, broad reasons of trust.

Republicans on Capitol Hill were torn over the move.

Sen. Richard Burr, North Carolina Republican and chairman of the Senate Select Committee on Intelligence, said he was “troubled by the timing and reasoning” of the decision. He said it confuses the committee’s investigation into Russia, which was relying heavily on information developed by the FBI.

“Director Comey has been more forthcoming with information than any FBI director I can recall in my tenure on the congressional intelligence committees,” Mr. Burr said. “His dismissal, I believe, is a loss for the bureau and the nation.”

Others, though, said Mr. Trump was within his rights.

“The effectiveness of the FBI depends upon the public trust and confidence. Unfortunately, this has clearly been lost,” said Senate Judiciary Committee Chairman Chuck Grassley, an Iowa Republican who said Mr. Comey had been slow to provide his panel with answers.

Mr. Comey’s firing could have been a challenge for Democrats, many of whom publicly blamed him for Mrs. Clinton’s election loss, with some demanding that President Obama fire him before the election.

They said they had lost confidence in him, saying he was wrong to reveal so many details about Mrs. Clinton while not revealing the probe of Trump campaign operatives.

Senate Minority Leader Charles E. Schumer, New York Democrat, acknowledged he had been one of those critics but said he never called for the president to fire Mr. Comey. He also said Mr. Trump’s timing will lead the public to suspect a cover-up.

Mr. Schumer said Mr. Trump called him Tuesday afternoon to alert him to the impending firing.

“I told the president, ‘Mr. President, with all due respect, you are making a big mistake,’” the minority leader said.

He joined fellow Democrats in saying the only path forward for Mr. Trump is for the probe to be taken over by a special prosecutor with complete independence.

Presidential counselor Kellyanne Conway said Mr. Trump showed his leadership as he “acted decisively.”

“He has lost confidence in the FBI director,” she said on CNN. “It has nothing to do with the campaign of six months ago. This has nothing to do with Russia, as much as somebody must be getting $50 every time the word is said on TV.”

Only one other FBI director has been booted in the agency’s history: William S. Sessions, a Reagan appointee, was fired by President Clinton in 1993 over purported ethics violations.

The upper echelon at the Hoover Building wasn’t surprised when Mr. Trump abruptly fired Mr. Comey. Rumors swirled for months that Mr. Comey was living on borrowed time.

Meanwhile, agents across the bureau were split over Mr. Comey’s ouster, although there was widespread agreement that a major change was needed to depoliticize the FBI and the Justice Department.

Agents didn’t necessarily blame Mr. Comey for the politicization. They blamed the Justice Department and state’s attorney’s offices. But there was recognition that Mr. Comey, a former federal prosecutor, was “a political animal.”

One veteran FBI official said morale couldn’t be lower.

“It’s in the toilet,” said the agent. “It’s because of the leaks. It’s because of the politicization. We used to be above the fray.”

⦁ Dave Boyer, S.A. Miller, Dan Boylan and Seth McLaughlin contributed to this report.

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