A federal judge in Georgia ruled Wednesday that the federal government did not have to return 2020 election records seized by the F.B.I., rejecting a request from Fulton County that the materials be returned.

After F.B.I. agents carried out an extraordinary seizure of about 660 boxes of records from Fulton County’s elections hub, county officials responded in early February by filing a lawsuit demanding the return of the documents and describing the search as unconstitutional.

But Judge J.P. Boulee of the Federal District Court in Atlanta wrote in his order that while he found elements of the case “troubling,” the county had not met the bar required for him to compel the government to return the records.

“This Court acknowledges that the events leading up to this case are, in a variety of ways, unprecedented,” Judge Boulee, who was appointed to the federal bench during President Trump’s first term, wrote in his 68-page order. But he said that the county had not shown that the federal government had displayed “callous disregard” for the constitutional rights of the county.

In the lawsuit, lawyers for Fulton County argued that the federal government’s action violated Fourth Amendment protections against unreasonable searches and seizures.

Judge Boulee’s decision was the latest episode in a saga animated by Mr. Trump’s push for redemption after his 2020 election loss in Georgia, where he lost to Joseph R. Biden Jr. by fewer than 12,000 votes. Georgia was one of a handful of swing states that Mr. Biden narrowly won on his way to the White House.

Mr. Trump has never accepted the outcome of the election, and he has filled the Justice Department and other federal agencies with officials sympathetic to his baseless claims that the 2020 election was stolen from him.

On Jan. 28, a team of F.B.I. agents, armed with a search warrant, descended on Fulton County to take ballots, voter rolls and scanner images from the county’s elections hub, a warehouse outside Atlanta.

At the time, Democrats and election security experts argued that the search was intended to intimidate the president’s opponents and undermine confidence in the U.S. election system.

Brad Raffensperger, the Republican secretary of state in Georgia and a candidate for governor, has described the investigation as a waste of time and government resources.

Unveiling the lawsuit in February, Robb Pitts, the chairman of the Fulton County Board of Commissioners, suggested that the federal government was attempting to take over elections, declaring that “our Constitution itself is at stake.”

On Wednesday, Mr. Pitts said in a statement that he “strongly” disagreed with Judge Boulee’s decision and suggested that the county might appeal the decision.

“Our fight has exposed the flawed affidavit and suspicious timeline of federal actions,” Mr. Pitts said in the statement. “We will continue, as always, to stand by our election workers and the voters of Fulton County. We intend to vigorously pursue all available legal options.”

The county said in the lawsuit that the search was apparently based on claims about the 2020 election that had been repeatedly debunked. At least 11 lawsuits challenging the 2020 election results in Georgia were filed, according to Fulton County court records. None produced evidence of widespread fraud or malfeasance.

“Claims that the 2020 election results were fraudulent or otherwise invalid have been exhaustively reviewed and, without exception, refuted,” the county’s complaint noted, adding that the effort was a “gross intrusion” on the state’s role in conducting elections.

Some Trump supporters cheered the ruling on Wednesday. Mark Davis, a contributing writer for The Federalist, a conservative publication, wrote in a social media post that the decision was a “major victory for election integrity.”

Wendy Weiser, vice president for democracy at the Brennan Center for Justice at N.Y.U. Law School, noted in an interview on Wednesday night that the search warrant process was kicked off by a well-known election denier. And the affidavit in support of the warrant relied on claims about ballots that have been widely debunked.

Ms. Weiser acknowledged that it was rare for judges to intervene and undo federal search warrants. “But if there’s ever an extraordinary time that this should happen, I think this was that,” she said.

The litigation has played out as the midterm election season has started in states across America, and as Republicans have raised concerns about election integrity and pushed for stricter rules at the ballot box.

Early voting for Georgia’s primary has already begun, with Election Day set for May 19. It was not immediately clear when or if the F.B.I. might return the 2020 election records.

A spokeswoman for Fulton County, Jessica Corbitt, said that as of Wednesday, none of the documents seized in January had been returned.

The F.B.I. declined to comment on Judge Boulee’s decision. The Justice Department did not immediately respond to a request for comment.

The Justice Department has also demanded the identities of every worker who staffed the 2020 election in Fulton County, according to court records. It is unclear what the Justice Department intends to do with the names.