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The Justice Department tried to intervene to represent President Trump against the lawsuit by the writer E. Jean Carroll, who claims he lied when he denied raping her.A federal judge ruled on Tuesday that President Trump can be personally sued for defamation in connection with his denial while in office of a decades-old rape allegation.

The judge, Lewis A. Kaplan of Federal District Court in Manhattan, rejected the Justice Department’s attempt to step into the case and defend the president. His ruling means that, for the moment, a lawsuit by the writer E. Jean Carroll can move forward against Mr. Trump, in his capacity as a private citizen.

Ms. Carroll has accused Mr. Trump of raping her in a department store dressing room in the 1990s. Her lawsuit claims he harmed her reputation when he denied the attack last year and branded her a liar.

Last month, the Justice Department abruptly intervened on Mr. Trump’s behalf in the suit, which had been filed in state court in New York, citing a law designed to protect federal employees against litigation stemming from the performance of their duties.

Under that law, the Federal Tort Claims Act, the department sought to move Ms. Carroll’s suit to federal court and to substitute the United States for Mr. Trump as the defendant — a move that would have likely led to the dismissal of the charges.

While the Justice Department has used the law to shield members of Congress from being sued for defamation over things they have said, the department has rarely, if ever, used it to grant immunity to a president.But Judge Kaplan, who was appointed by President Bill Clinton in 1994, ruled against the department’s maneuver, saying Mr. Trump was not acting in his official capacity when he denied the accusation.

“His comments concerned an alleged sexual assault that took place several decades before he took office, and the allegations have no relationship to the official business of the United States,” the judge wrote. In a statement issued shortly after the decision, Ms. Carroll said she could now return to the task “of getting the truth out.”

“When I spoke out about what Donald Trump did to me in a department store dressing room, I was speaking out against an individual,” she said. “When Donald Trump called me a liar and denied that he had ever met me, he was not speaking on behalf of the United States.”

In dueling court papers filed earlier this month, the two sides had debated the central issue raised by the Justice Department’s gambit: Could Ms. Carroll continue to pursue Mr. Trump in his personal capacity, or was he, as the government claimed, immune because he denied the accusation while in office and in his official role as president?

Ms. Carroll argued that the Federal Tort Claims Act was generally designed for lower-level government employees and did not apply to Mr. Trump — or to any other president. She also said that Mr. Trump, in any case, was not acting in his official role when he denied her claims.

The Justice Department argued that Mr. Trump’s statements denying the rape accusation were an official act because he “addressed matters relating to his fitness for office as part of an official White House response to press inquiries.”

The Justice Department declined to comment on the ruling, and it remained unclear if the department would appeal. A lawyer for Mr. Trump did not respond to a request for comment. The judge’s decision came only one week before the presidential election, and it was impossible to know how any possible change in the White House would affect the suit.

Ms. Carroll’s suit against the president will now continue in federal court, her lawyer, Roberta A. Kaplan said.

The department’s move to step into the Carroll case had come at the direct request of the White House, according to Attorney General William P. Barr. Mr. Barr’s department has also intervened in other matters involving Mr. Trump, including the criminal case of his former national security adviser Michael T. Flynn. In the Flynn case, Mr. Barr’s department sought to drop the prosecution — a move that a federal judge has held up while he is scrutinizing it.

The lawsuit Ms. Carroll initially filed in State Supreme Court in Manhattan accused Mr. Trump of lying in several public statements last year when he firmly denied he had attacked her in a dressing room in Bergdorf Goodman, the high-end Manhattan store, in the mid-1990s.

According to Ms. Carroll’s account in a book and magazine article, Mr. Trump stopped her in the store and said, “Hey, you’re that advice lady!”

She claimed that Mr. Trump then accompanied her into the dressing room, threw her against a wall, pulled down her tights and raped her.

Shortly after the account came out, Mr. Trump denied that he had ever met Ms. Carroll and accused her of lying, adding, “She’s not my type.” In a written statement, Mr. Trump also said Ms. Carroll was “trying to sell a new book.” He added, “It should be sold in the fiction section.”

In her lawsuit, Ms. Carroll said that Mr. Trump’s denials had harmed her reputation, causing her to lose the good will and support of her readers. Mr. Trump, initially represented by private lawyers, sought to delay the case on the grounds that as a sitting president he was completely immune to civil lawsuits in state court.

But in August, a New York State judge, Verna L. Saunders, denied his request. She cited a ruling by the United States Supreme Court this summer, which rejected a claim by Mr. Trump that, as president, he was immune from a state criminal investigation. That dispute arose after the Manhattan district attorney’s office subpoenaed Mr. Trump’s accountants for his tax returns.

Justice Saunders’ ruling also put additional pressure on Mr. Trump by opening the door not only to requiring him to be deposed before the November election, but also to compelling him to give a DNA sample. Ms. Carroll saved the dress she wore during the encounter and maintains that it has her attacker’s genetic material on it.