Senate Democrats called on President Reagan yesterday to ask Secretary of Labor Raymond J. Donovan to "step aside" until all the allegations linking him to organized crime and union corruption have been resolved satisfactorily.

Senate Minority Leader Robert C. Byrd (D-W.Va.) made the request to Reagan in a letter that was approved unanimously at yesterday's weekly Senate Democratic Conference.

The action came in the wake of a disclosure that the incoming Reagan White House was told by the FBI in January, 1981, on the day of Donovan's first Senate confirmation hearing, that Donovan had "close personal and business ties with known La Cosa Nostra figures."

Sen. Orrin G. Hatch (R-Utah), chairman of the Senate Labor Committee, which considered Donovan's nomination, said he never saw the one-page FBI report until last week.

In a brief speech on the Senate floor yesterday afternoon, Byrd said he wanted to emphasize "the extreme urgency" that Senate Democrats attach to the matter. "The American people," he said, "must have confidence in the president's cabinet."

At the White House, however, there was no indication that the president's confidence in Donovan had diminished.

Asked earlier in the day if Reagan has "complete confidence" in Donovan, White House spokesman Larry Speakes said, "Yes." And when asked if Donovan's resignation had been requested, Speakes said, "I've not heard it discussed."

Special prosecutor Leon Silverman, who was appointed in December under the Ethics in Government Act, is reportedly nearing the end of his investigation of Donovan's business activities before he joined the Cabinet.

The allegations range from charges of involvement in bid-rigging and union payoffs on behalf of his New Jersey construction company to asserted ties to organized crime.

Silverman also asked the FBI over the weekend to begin an investigation under the obstruction-of-justice statute into the gangland-style slaying of a potential witness in the Donovan case. The body of Fred Furino, 52, was found in the trunk of his car in Manhattan Friday. He had a bullet hole in his forehead.

Furino, a onetime New Jersey Teamsters official, was interviewed by Silverman several times before Furino's disappearance June 3, and may have testified before the federal grand jury in Brooklyn that has been assigned to the Donovan probe.

According to a confidential FBI report at the time of Donovan's nomination, a bureau informer said Furino was a sometime "bagman" for a now dead New Jersey mobster named Salvatore Briguglio and occasionally "picked up money" from Donovan on Briguglio's behalf.

Allegations linking Donovan to Briguglio, a reputed Mafia hit man, have dogged Donovan since his confirmation hearings, but he has denied them steadfastly.

As for social and business ties to organized-crime figures, Donovan said at his final hearing on Jan. 27, 1981, that he did not have any, "at least not to my knowledge. None has been identified to me as being organized-crime people."

The two-page letter to Reagan recommending a leave of absence for Donovan was endorsed by all 36 Senate Democrats at yesterday's policy session. Byrd signed it as chairman of the Senate Democratic Policy Committee.

In it, Byrd said that "Democrats have been restrained in our comments on the Donovan case" in the belief that, "Except in the most extreme circumstances, any action in the matter should await the findings of the special prosecutor.

"However," the letter continued, "we believe those extreme circumstances now exist . . . . Mr. President, we believe the time has come for you to ask Mr. Donovan to step aside until all of the issues raised by this investigation have been satisfactorily resolved."

Byrd also voiced alarm about reports that the administration is considering either repeal of, or significant cutbacks in, the Ethics in Government Act, including elimination of the requirement that top officials make their financial holdings public. The administration also has voiced dissatisfaction with the special-prosecutor provisions of the law.

Byrd urged Reagan instead to "affirm your support for that law, which grew out of the abuses of Watergate and which has done so much to restore public confidence in government."

Byrd wondered in his floor speech how Donovan could "devote his full attention to the tremendous issues relating to the lives and well-being of millions of Americans when he must respond day after day to new allegations about 'mob' connections which continue to appear in the press."

"I don't know if any of these charges are true or not," Byrd said. "I certainly hope they are not." But he said he thought it would be "in the best interests of our country" for Donovan to step aside until the allegations have been resolved.

Hatch also has pledged an investigation by his committee, once Silverman issues his report, of the role of the FBI and the White House in last year's investigation of Donovan.

The man in charge of that inquiry, FBI Executive Assistant Director Francis M. Mullen, has had his nomination to head the Drug Enforcement Administration shelved as a result.