A federal judge in Atlanta on Tuesday cast serious doubts on the Justice Department’s efforts to reinvestigate President Trump’s false claims that he was cheated out of victory in the 2020 election, saying that the five-year statute of limitations for any possible crimes arising from the race had “long expired.”

The finding by the judge, William M. Ray II, came in a sternly worded order that quashed a grand jury subpoena that prosecutors had issued in April. The subpoena sought what the judge described as a “staggering” amount of personal information about thousands of election workers in Fulton County, Ga., who took part in the administration of the count — and recount — of the vote in 2020.

The judge’s determination that prosecutors had missed their window to bring charges stemming from the 2020 election was a decisive blow against the Justice Department’s attempts to bolster one of Mr. Trump’s loudest and longest-lasting falsehoods: that he lost the race to Joseph R. Biden Jr. only because of widespread fraud.

In service of the president’s claims, federal law enforcement has already undertaken an extraordinary series of investigative steps. In January, the F.B.I. sent agents to seize hundreds of boxes of records, including original ballots, from a Fulton County election warehouse. And just last week, the bureau deployed an army of F.B.I. analysts to sort through the seized materials.

While Judge Ray’s ruling did not stop prosecutors from pursuing their inquiry in Fulton County, it appeared to throw a major roadblock in the case by putting in writing a finding that it was essentially too late for anyone to face indictment. The ruling also raised questions about the underlying purpose of the inquiry, which election integrity experts have long claimed was simply to erode trust in elections in the minds of American voters.

“These records, even if they lead to the D.O.J. finding individuals who worked for Fulton County in the 2020 election who support the theory that the 2020 election was not fair, would not lead to information that could be used to charge anyone with anything, at least not any viable charge,” Judge Ray wrote. “That is because the statute of limitations for any possible crime arising from the 2020 election has long expired.”

In his ruling, Judge Ray, who was appointed by Mr. Trump, also found that the subpoena for the workers’ information was “an arbitrary fishing expedition” by the department and amounted to an “unreasonable” use of the invasive powers afforded to grand juries.

“Everyone, whether you support the president or you do not, or whether you believe the 2020 election was fair or believe that it was not, should be concerned about the D.O.J.’s ability to utilize the power of the grand jury to appropriate your private information without a legitimate purpose,” Judge Ray wrote.

Few presidential contests in modern American history have been as thoroughly investigated as the 2020 election. Over more than five years, every conspiracy theory from Mr. Trump and his allies — including false claims about election workers, mail ballots and election machines — has been examined, re-examined and ultimately debunked by election officials from both political parties and, in many cases, by members of Congress, judges and law enforcement.

Fulton County, which encompasses most of Atlanta, has long been a Democratic stronghold and is the most populous county in Georgia. The unproven claim that county election workers somehow helped Democrats steal the 2020 election was a major part of a wide-ranging but ultimately fruitless effort by Mr. Trump and his supporters to reverse Mr. Biden’s victory in the state.

Judge Ray’s ruling was the latest embarrassment for the Justice Department, which has struggled in recent months with using grand juries in several criminal inquiries, many involving Mr. Trump’s political agenda. Prosecutors in U.S. attorney’s offices across the country have repeatedly failed to persuade grand jurors that charges were warranted in politically tinged cases and have also been accused of severe misconduct when presenting indictments to grand juries.

Typically prosecutors enjoy wide latitude when issuing grand jury subpoenas, and it was once exceedingly rare for judges to step in and quash them. But that has happened an unusual number of times to the Justice Department under Mr. Trump.

Two weeks ago, for instance, a federal judge in Minnesota blocked a flurry of subpoenas issued to Gov. Tim Walz and other elected Democrats, ruling they were part of an improper effort to retaliate against the officials for standing up to Mr. Trump’s immigration crackdown in the state.

That decision followed a similar one in March by a federal judge in Washington who quashed subpoenas issued during an investigation into Jerome H. Powell, the Federal Reserve chair at the time, saying they had been sent only to “harass and pressure” Mr. Powell into yielding to Mr. Trump’s desire for lower interest rates.

It was never entirely clear why the Justice Department issued the sprawling subpoena in Fulton County seeking the names, addresses, email addresses and phone numbers for every county employee — both paid and volunteer — who worked on the 2020 election. Judge Ray wrote that prosecutors claimed they were “engaged in legitimate law enforcement activities” and wanted to re-examine Mr. Trump’s longstanding allegations that his defeat was based on fraud.

But while the judge acknowledged that a grand jury could be part of that inquiry, he cautioned that prosecutors do not have “the right to use the grand jury to do whatever the D.O.J. wants.”