Justice Department officials said yesterday they will turn over information on their aborted investigation of Teamsters union President Jackie Presser to a federal grand jury in Cleveland, which plans to consider whether government agents or prosecutors acted illegally in the way they handled the politically sensitive case.

The department's announcement came in response to a request from a federal judge, who temporarily freed Presser's uncle, Allen Friedman, from a Texas prison yesterday. U.S. District Court Judge Sam H. Bell ordered the grand jury to investigate whether government officials acted improperly when they failed to disclose the FBI's confidential relationship with Presser when Friedman was convicted of embezzlement two years ago.

Spokesman John K. Russell also said the Justice Department has elevated an internal FBI inquiry into the handling of the case to "a much higher level." He said that the probe is being handled by the department's Office of Professional Responsibility, a watchdog unit, and that it could lead to criminal charges. Russell said the department will comply with the judge's order and turn over its findings to the Cleveland grand jury, which indicted Friedman and had been conducting the investigation of Presser.

Russell also said that the FBI is investigating death threats against Presser and Bell that were described in a letter from a prison inmate to the judge.

The Justice Department dropped a 32-month probe of Presser last month after belatedly learning that the FBI had authorized Presser to put several "ghost employes" on the Teamsters payroll as part of another investigation, according to federal law enforcement sources. Friedman, 63, who received $165,000 in union payments approved by Presser, was convicted of being one of the ghost employes who allegedly did no work.

Bell granted a new trial yesterday for Friedman, who has served 11 months of a three-year sentence, and allowed him to remain free on personal bond. The government moved to dismiss the charges, but Friedman's attorneys objected, saying they want a new trial to clear their client's name.

Bell delayed a final ruling until at least Sept. 20. Prosectors had said they would agree to drop the charges against Friedman rather than be forced to disclose the government's relationship with Presser at a new trial. "I think it's time we all dispel the shadow of rumor and innuendo and shine the light of truth on the happenings before the last trial," Bell said.

It is considered improper for government officials to refuse to give defense lawyers information that could aid their client. In this case, however, it is not clear whether FBI agents who worked with Presser fully disclosed the arrangement to their Justice Department superiors or to the prosecutors in Cleveland.

Presser's attorney has maintained that the Teamsters chief was not an informer for the FBI.

Justice Department officials have repeatedly refused to discuss the investigation of Presser, the only major labor leader to support President Reagan. The department took over the probe after it was begun by Labor Department investigators.

"I was always innocent, and I'm going to prove that I'm innocent," Friedman said after the hearing. He was put on the Teamsters payroll as a $1,000-a-week business agent after merging his union with Presser's Cleveland local.

One of Friedman's lawyers, Jack Levin, said yesterday that he may file a civil suit against the Justice Department, seeking monetary damages for what he called "governmental misconduct." Even if a new trial is not granted, he said, a civil suit would enable him to obtain documents about the government's relationship with Presser.

"They intentionally set up a crime to harass and injure this man," Levin said. "How does one arm of the government do something without the other arm knowing? This is going to go back to Washington. Someone there had to know something."

Bell asked the government to look into the death threats described in a letter from an inmate at the Fort Worth prison where Friedman was being held. "I am in possession of information which involves a planned assassination attempt to your life, as well as members of your family," the inmate wrote Bell. " . . . I have no doubt that these people are serious in this matter and they will not rest until they have taken your life."