White House counsel Fred F. Fielding has warned senior presidential aides to maintain an "arms-length relationship" with new Teamsters union President Jackie Presser on grounds that he is under active investigation by the Labor Department in a major union embezzlement case, administration officials have disclosed.

They said that as a result of this warning Presser--who is far and away the most important labor figure in the Reagan camp, to the point of having been honored by Secretary of Labor Raymond J. Donovan and senior White House officials at a private dinner in Georgetown on June 20--no longer will be invited to the White House for state dinners or other social events.

But White House officials said that the administration would continue to maintain close political ties with the Teamsters and to consult with Presser.

As an example, presidential assistant Craig L. Fuller said a trucking deregulation bill remains "on hold" despite President Reagan's philosophical commitment to it, largely because of Teamsters objections.

Presser is one of the few labor leaders who supported Reagan in 1980 and one of a diminishing group of such officials expected to support him if he runs for a second term.

White House political adviser Edward Rollins and public liaison director Faith Ryan Whittlesey said recently that they look on such support as an important element in any Reagan reelection coalition in 1984.

Donovan, for his part, maintained that Presser should be "given the benefit of the doubt" when he says he wants to clean up his union, and added that he saw nothing wrong with inviting the Teamsters president to state dinners.

Speaking of the concern that Fielding and others at the White House have expressed about the closeness of the relationship, Donovan said: "I know they're cautious and should be cautious because these things have a way of coming back to haunt you. But in my America, as secretary of labor, you have to continue to deal with the Teamsters."

Presser, a frequent White House visitor in recent months, has met twice with Rollins to discuss political strategy, including a prospective rally that would advertise how Reagan has "put America back to work."

"Jackie Presser has opened the door to labor for us," said one official in discussing the importance of the Teamsters to a Reagan second-term campaign. "If Ronald Reagan has a problem with that, it is less than the problem he has with the image of being a rich man's president."

Presser also has met with Whittlesey, who said she would like him to become involved in her office's efforts to explain administration policy in Central America. "I don't think you can turn your back on a union that has been so supportive and so large," Whittlesey said.

Nonetheless, administration officials said that Fielding issued a pointed warning to White House chief of staff James A. Baker III, deputy chief of staff Michael K. Deaver and White House counselor Edwin Meese III that it would be imprudent to invite Presser to any more state dinners.

Presser turned down an invitation to a state dinner in June, saying he had a scheduling conflict. A senior White House official said another invitation was "in the works" but would not be issued because of Fielding's warning.

Presser, 56, long has been the target of allegations that he has ties to organized crime. Whenever they are raised, Presser responds that he has never been indicted and challenges his accusers to "name names and present evidence."

The investigation that has touched off White House concern centers on an alleged "ghost-employe" embezzlement scheme involving both Presser's local 507 and an affiliated bakery workers' union in Cleveland.

White House officials long have been aware of this investigation, which was launched by the Labor Department in 1981. But it acquired new significance last month after Presser's uncle, Allen Friedman, was indicted as one of five alleged non-working "ghost employes" who had been receiving a salary illegally. Friedman, charged with embezzling $165,000, said subsequently in an NBC news interview that he was prepared to incriminate his nephew.

"Jackie Presser should have been in jail dozens of times, going back 30 years," Friedman said. "He thinks I won't testify against him . . . . But I don't like the things he's done, double-crossing me, doing what he's doing to the working people."

According to a Labor Department affidavit filed last year in U.S. District Court, the investigation focused on charges that Presser, as secretary-treasurer of local 507, and Harold Friedman, the local's president and no relation to Allen Friedman, embezzled union fees by signing salary checks to people who didn't work for the union. The affidavit said that Allen Friedman had refused to tell his story to a grand jury. Officials said it was his apparent change of heart that prompted White House concern about what one of them called "cozy relationships" between Presser and administration figures.

On June 20, Presser was guest of honor at a Georgetown Club dinner attended by Donovan, Rollins, long-time Reagan intimate Lyn Nofziger and Senate Labor Committee Chairman Orrin G. Hatch (R-Utah). Meese and Sen. Paul Laxalt (R-Nev.), general chairman of the Republican Party and Reagan's closest friend on Capitol Hill, dropped by for a reception beforehand. One official said that what he called the "new guidelines" laid down since the indictment of the union officials would preclude further such social events.

But the administration does not want to appear to be snubbing Presser, in particular because of the revitalized effort the AFL-CIO is expected to undertake for the Democrats in 1984 and because persistent unemployment has hurt Reagan among blue-collar workers, who gave him more than 40 percent of their votes in 1980.

"Let's face it, we haven't done much with labor," said one official. "And Presser is the key for us. Do you just walk away from a union president who has such a tremendous political network or do you stand by your friends?"

Presser, who is considered far more sophisticated politically than past Teamsters presidents, is regarded as a special friend of the administration because he pushed through the endorsement of Reagan in a fiery speech at a Teamsters executive board meeting at La Costa in 1980.

In mid-1980 Reagan appeared in Columbus at a Teamsters event organized by Presser in which Reagan first said that President Carter had plunged the economy into a "depression."

"We're not going to forget that Jackie Presser is the person most responsible for Teamster endorsement of Reagan in 1980," said a Republican who was close to the process. "When other labor unions were vilifying Reagan, the Teamsters helped. They are not popular with the general public, but no one thinks they are patsies. They're the largest union, they're tough, they don't look like they're easily fooled. They have public relations value for Ronald Reagan."

Reagan also has been involved recently with another union that has had legal problems. On July 18, he became the first U.S. president to address the national convention of the International Longshoremen's Association, where he praised union president Thomas W. (Teddy) Gleason, who in 1981 told a Senate committee that he had invoked the Fifth Amendment and refused to answer questions before a federal grand jury investigating corruption in his union.

"I'll tell you what I've always liked about Teddy. He sticks by his union," Reagan told the ILA. "He sticks by his friends and he sticks by his country, the kind of integrity and loyalty that is hard to come by today."

FBI Director William H. Webster has been outspoken about corruption in the ILA, and more than 30 union officials have been convicted on charges including extortion, embezzlement, bribery, perjury and racketeering in the last four years.

Both Gleason and Presser oppose the administration's anti-racketeering bill that would force persons convicted of a felony to leave union offices immediately for 10 years.

When he went to Camp David, three days before the ILA speech, Reagan carried material with him, prepared by Fielding, that provided background information on union corruption in the ILA, officials said. It is not known if he read it.