WASHINGTON — As Republicans continued on Sunday to defend former President Donald J. Trump after an unprecedented F.B.I. search of his residence in Florida, deep fissures were visible in the party’s support for law enforcement amid a federal investigation into Mr. Trump’s handling of top secret documents.

Immediately after the search, congressional Republicans, including members of leadership, reacted with fury, attacking the nation’s top law enforcement agencies. Some called to “defund” or “destroy” the F.B.I., and others invoked the Nazi secret police, using words like “gestapo” and “tyrants.”

On Sunday, more moderate voices in the party chastised their colleagues for the broadsides against law enforcement, making a more restrained case for defending Mr. Trump while also carrying out oversight of the Justice Department.

Many Republicans called for the release of the affidavit supporting the search warrant that was executed last Monday, which would detail the evidence that had persuaded a judge there was probable cause to believe a search would find evidence of crimes. Such documents are typically not made public before charges are filed.

“It was an unprecedented action that needs to be supported by unprecedented justification,” Representative Brian Fitzpatrick, Republican of Pennsylvania and a former F.B.I. agent, said on CBS’s “Face the Nation. But he added, “I have urged all my colleagues to make sure they understand the weight of their words.”

The calls for a more cautious tone came as threats emerged against law enforcement. A gunman on Thursday attacked an F.B.I. office in Cincinnati, and on Friday, the Department of Homeland Security distributed an intelligence bulletin to law enforcement around the country that warned of “an increase in threats and acts of violence, including armed encounters, against law enforcement, judiciary and government personnel” after the search.

“The F.B.I. and D.H.S. have observed an increase in violent threats posted on social media against federal officials and facilities, including a threat to place a so-called dirty bomb in front of F.B.I. headquarters and issuing general calls for ‘civil war’ and ‘armed rebellion,’” said the bulletin, which was obtained by The New York Times.

Adding to the sense of alarm, another gunman crashed a car into a barricade outside the Capitol around 4 a.m. on Sunday. After he exited the car and it became engulfed in flames, he shot into the air several times before killing himself, the Capitol Police said.

Mr. Fitzpatrick said he had begun checking in with his former colleagues at the F.B.I. “to make sure they were OK.”

“We’re the world’s oldest democracy, and the only way that can come unraveled is if we have disrespect for institutions that lead to Americans turning on Americans,” he said, adding, “A lot of that starts with the words we’re using.”

Republicans have struggled to coalesce around a unified strategy to respond to the F.B.I.’s search of Mar-a-Lago, Mr. Trump’s home in Palm Beach, Fla., amid daily revelations and quickly shifting explanations, excuses, defenses and false accusations by the former president.

On Friday, a federal judge unsealed the warrant authorizing the search and an inventory of items removed from the property by federal agents. The list showed that the F.B.I. had retrieved 11 sets of classified documents as part of an inquiry into potential violations of the Espionage Act and two other laws.

Some of the documents were marked “classified/TS/SCI” — shorthand for “top secret/sensitive compartmented information.” Such information is meant to be viewed only in a secure government facility.

Mr. Trump and his allies have argued that former President Barack Obama also mishandled documents (an allegation quickly dismissed as false by the National Archives); that the judge who signed the warrant authorizing the search must have been biased; that the F.B.I. might have planted evidence; that the documents were covered by attorney-client or executive privilege; and that Mr. Trump had declassified the documents.

The former president has worked to cash in on the search.

Mr. Trump’s political action committee has been furiously fund-raising off the F.B.I. search, sending out at least 17 text messages to donors since Tuesday. “The Dems broke into the home of Pres. Trump,” one read. “This is POLITICAL TARGETING!” another alleged. “THEY’RE COMING AFTER YOU!” a third said.

Donald Trump Jr., the former president’s son, wrote another fund-raising email on Sunday: “The witch hunt continues…The FBI’s raid of Mar-a-Lago was a DISGRACE. In fact, it’s UNFATHOMABLE.”

On Saturday, Senator Rand Paul, Republican of Kentucky, also called for the repeal of the Espionage Act, one of the statutes that prompted the investigation.

But the shifting explanations have made it difficult for Republicans, many of whom are eager to please the former president, to come together with a unified defense. They are divided about whether to attack the nation’s top law enforcement agencies and how aggressive to be in those attacks.

Representative Marjorie Taylor Greene, a Georgia Republican whom the National Republican Congressional Committee is featuring in fund-raising appeals, has begun selling merchandise that says “Defund the F.B.I.”

That is a much different approach from Representative Michael R. Turner of Ohio, the top Republican on the Intelligence Committee, who defended Mr. Trump on Sunday.

Republicans on the committee have said they continue to support law enforcement. Still, they said that tough questions remained for Attorney General Merrick B. Garland about his decision to take the bold step of ordering a search of the former president’s home, and they promised to hold the Justice Department accountable.

“Clearly, no one is above the law,” Mr. Turner said on CNN’s “State of the Union.” “Donald Trump is not above the law. And Attorney General Garland is not above the law, either. And Congress has the powers of oversight. He needs to comply.”

Mr. Turner said he had not been convinced “whether or not this actually is classified material and whether or not it rises to the level of the highest classified material,” despite the documents released by the court.

“I’d be very surprised if he has actual documents that rise to the level of an immediate national security threat,” Mr. Turner said.

Two of the laws referred to in the search warrant, however, make the taking or concealment of government records a crime regardless of whether they are related to national security. The third, which bars the unauthorized retention of material with restricted national security information, applies whether or not the material is classified.

The Republican leaders in the Senate and the House, Senator Mitch McConnell of Kentucky and Representative Kevin McCarthy of California, have also said that Mr. Garland needs to provide answers.

Mr. Garland, for his part, held a news conference on Thursday defending the way the Justice Department has handled the case.

“Upholding the rule of law means applying the law evenly, without fear or favor,” he said. “Under my watch that is precisely what the Justice Department is doing.”

The White House, trying to avoid the appearance of partisan interference, has been reluctant to comment on the investigation. “We do not interfere. We do not get briefed,” Karine Jean-Pierre, the White House press secretary, said on ABC’s “This Week,” adding, “We’re going to let Merrick Garland speak for himself and his department.”

But other Democrats immediately seized on Republicans’ anti-law enforcement statements.

“I thought in the old days the Republican Party used to stand with law enforcement,” Senator Amy Klobuchar, Democrat of Minnesota, said on NBC’s “Meet the Press.” “And I hope some of them do today because this kind of rhetoric is very dangerous to our country.”

She pointed out that when she reviews classified documents she must do so in a secure room. “I can’t even wear my Fitbit,” she said.

Representative Adam B. Schiff, Democrat of California and the chairman of the Intelligence Committee, has called for the director of national intelligence to conduct an “immediate review and damage assessment” and provide a classified briefing to Congress about the potential harm done to national security by Mr. Trump’s handling of documents.

“The fact that they were in an unsecure place that is guarded with nothing more than a padlock or whatever security they had at a hotel is deeply alarming,” he said on “Face the Nation.”

Senator Rob Portman of Ohio, the top Republican on the Homeland Security Committee, called on his panel to scrutinize Mr. Garland’s actions.

“Never has a former president and potential political opponent to the sitting president been subject to such a search,” Mr. Portman said in a statement. “The attorney general and the F.B.I. should now demonstrate unprecedented transparency and explain to the American people why they authorized the raid.”

Senator Mike Rounds, Republican of South Dakota, took a similar approach.

“I’m not one of the individuals out there that says that, you know, ‘Immediately attack the F.B.I. or the Justice Department,’” he said on “Meet the Press.”

“But,” he added, “I think it’s very important long term for the Justice Department, now that they’ve done this, that they show that this was not just a fishing expedition.”