Flashing a smile and a thumbs-up salute, Raymond J. Donovan, the embattled Secretary of Labor, yesterday stepped briefly into public view to say that he is "extremely pleased and certainly not surprised" that a special prosecutor's report had concluded there was insufficient evidence to prosecute him on charges of mob-linked corruption.

"The special prosecutor has confirmed what I told you all along--that none of these allegations would prove to be true," Donovan told an audience of reporters and cheering supporters at the Labor Department.

His intention now, he said, is "to devote all my time and all of my energies to the task that President Reagan asked me to do 18 months ago."

White House sources say that Donovan still is likely to face pressure to resign, but there was no indication of this from President Reagan, who, according to one aide was, "pleased as hell" with the report.

When asked at the daily White House briefing whether the president still has "full confidence" in Donovan, press aide Larry Speakes responded, "I have not heard him say otherwise."

Later, Speakes called reporters back in to say that the president is "extremely pleased" about the special prosecutor's report.

"The president called Secretary Donovan this afternoon to express his pleasure," Speakes said.

Several White House officials have expressed a view that Donovan is a political liability to the president. Some have said privately they hope that Donovan himself will become aware of this and resign. Even some of Donovan's defenders are concerned that the long-awaited, voluminous report, with its cautiously worded finding of "insufficient credible evidence," will not be enough to lay the secretary's problems to rest.

Still, Reagan intimates cautioned against leaping to the conclusion that Donovan is leaving.

Reagan, who doesn't like to fire people, has just gone through the traumatic resignation of Secretary of State Alexander M. Haig Jr. and doesn't want to face another decision of this nature, according to one source. Some administration officials hope that Donovan will do what Haig did and take the decision out of the president's hands by deciding on his own to leave.

Pending any decision by Donovan, it appears likely that the labor secretary can survive White House displeasure because Reagan still believes in him. As White House counselor Edwin Meese III, a Donovan defender, quipped last week: "If you've only got one friend in the White House, that's the friend to have."

On Capitol Hill, Sen. Orrin G. Hatch (R-Utah), chairman of the Labor Committee, said he is "pleased" with the report but would reserve more detailed comment until he has read all four of its volumes.

"As I've expressed many times, the secretary should be given the benefit of any doubt," he said. In answer to a question later, Hatch added that he had no apologies to make to Donovan for his role in the investigation.

"I don't think anybody owes anybody an apology . . . ," he said.

His committee still intends to look into the FBI's failure to provide information to the Senate during Donovan's confirmation hearings that it had provided to the White House, he said. Hatch offered to invite Donovan to give the committee his side of the picture "anytime."

Donovan, one of 12 children in a poor Catholic family, made millions by helping to build Schiavone Construction Co. into a major contractor. He attracted the eye of the Reagan presidential campaign by raising over $500,000 for the candidate.

Hatch initially supported Donovan's controversial nomination, but later joined Sen. Edward M. Kennedy (D-Mass.) as an aggressive interrogator of the wealthy former construction executive. He has recently suggested that Donovan should resign.

Donovan matched Hatch's combative stance with one of his own, as the headlines continued to link his name, month after month, with organized crime. While Donovan spoke out in his own defense, once calling one of his accusers "murdering slime," his New Jersey construction firm decided to fight fire with fire and hired its own investigators to investigate the Senate investigators, further angering Hatch, Kennedy and others.

Donovan blames his problems in part on what he calls "the New Jersey syndrome."

"If you are in the contracting business in New Jersey, you're indicted, and if you're Italian, you're convicted," he has said.

In an exclusive interview in the Jersey Journal this week, he said the charges that he has ties to organized crime are actually attacks on Italian Americans, spearheaded by Democrats who are "out to get me."

"They're demeaning 20 million people because of a few rotten hoodlums who happen to be Italian."

Yesterday, he blew a kiss to his supporters, thanking them and adding, "It is a relief to me and my family to see this issue resolved once and for all."