President Reagan last night expressed warm and sympathetic support for Secretary of Labor Raymond J. Donovan, saying: "Certainly I'm sticking with him. . . . This case is closed."

The president was asked at his televised news conference if Donovan were a political embarrassment.

In his first comment on Donovan's fate since a special prosecutor's report was released Monday, Reagan responded: "Now, why should someone be an embarrassment who has been attacked and undergone what he has undergone all these months, and then a thousand pages of investigatory report says there never was any substantiation for those charges, as he had said in the beginning there would be none?"

The six-month investigation found "insufficient credible evidence" to indict Donovan on a spate of charges that he had ties to organized-crime figures and had been involved in corrupt labor practices while an executive of a New Jersey construction company.

"I think it would be the most unfair thing in the world for anyone to think he has been anything but unfairly and unjustly assailed," Reagan said.

Asked if the case were closed as far as he was concerned, the president said, "You bet."

The White House altered the endorsement strategy late yesterday in order to bolster its chance of ending speculation that Donovan is about to be forced out by presidential aides who consider him a political liability, White House sources said.

Early in the day, deputy White House press secretary Larry Speakes and other top officials had indicated their intention to release a statement about Donovan on Reagan's behalf.

However, at a meeting of Reagan and top aides, it was decided that such an approach would seem lukewarm and would only fuel the charges of recent days that the White House was trying to "distance" the president from his beleaguered labor secretary. The president reportedly agreed that he should deliver the rhetorical embrace personally.

While the special prosecutor's four-volume report removed the threat of indictment, it has failed to quell doubts about Donovan's political viability as a Cabinet officer. White House officials, like many others, had reserved substantive comment on the matter until they had reviewed the findings.

Some White House sources have said privately that Reagan, having just lost a secretary of state, wants to avoid any more top-level upheavals this pre-election season.

In another development yesterday, an attorney for Donovan's firm, Schiavone Construction Co. of Secaucus, N.J., said that the company's counterinvestigation of the Senate Labor Committee had been halted.

Offering no apology, attorney Theodore Geiser reportedly told the Associated Press in a telephone interview that Schiavone had acted properly in hiring private investigatorsto check out the congressional investigators who were pursuing the Donovan charges independent of the special prosecutor.

Regarding the resulting fury in Congress, and calls for Donovan's departure, Geiser was quoted as saying: "I'm sorry they're so sensitive. My clients are sensitive, too."

Clear signals of dissatisfaction continued to come from Capitol Hill. Senate Minority Leader Robert C. Byrd (D-W.Va.) yesterday sent a letter to the president requesting any material on Donovan and other administration officials that the FBI supplied to the White House but withheld from the Senate committees constitutionally responsible for confirming nominations.

Byrd said in the letter that he finds "very disturbing" the recent published reports that the FBI had withheld from the Senate Labor Committee information compiled during its background check that seemed to link Donovan to underworld figures.

Labor Committee Chairman Orrin G. Hatch (R-Utah) has reaffirmed that panel's intention to investigate the FBI's role in the matter.

Also yesterday, Reed Larson, head of the National Right to Work Committee, roundly endorsed Donovan, saying he "must not be driven out of public service by mob action."