Labor Secretary Raymond J. Donovan said in Labor Day appearances that he has never had a thought of resigning his Cabinet post in the face of criminal allegations and believes he will be a "political asset" for Republicans in the fall election campaigns.

In one of his rare public appearances during the year and a half he has been under investigation, Donovan took to the air on CBS, ABC and the Cable News Network yesterday with the message that the American worker "should please have hope . . . that the Reagan economic program is beginning to work."

But in all three interviews, Donovan found himself mainly fielding questions about the special prosecutor's prolonged investigation into the dealings of his New Jersey construction company.

Despite his trouble, Donovan said, "I'm going to be out campaigning" for Republicans this fall. Donovan said that regardless of recurring calls for his resignation, he is not a political liability to the Reagan administration during the election year.

"As a matter of fact, I honestly can tell you, looking you straight in the eye, that I, Ray Donovan, believe I'm a political asset," he said on the CBS Morning News (WDVM).

Reminded that special prosecutor Leon Silverman has wondered how Donovan can be so certain Silverman will exonerate him, the secretary said: "Before I even heard the name Leon Silverman, the special prosecutor . . . I, Ray Donovan, knew that I am guilty of none of those charges."

Asked why, then, the investigations and charges against him continue, Donovan said he hoped someone would win a Pulitzer Prize in finding out. Donovan was investigated by the special prosecutor and cleared on June 28. But before the prosecutor officially closed the investigation he got new evidence, not yet revealed. There was another complication Aug. 25 when Nat Masselli, who had testified in the Donovan case, became the victim of a mob-style killing.

When asked whether he could be an effective secretary of labor, and if the investigations had taken their toll, Donovan acknowledged that the investigations were distracting and taking time away from his job.

But he said, "I learned as a young man that self-pity is something that saps your energy and does you no good. I allow myself five minutes a day to feel sorry for myself. The rest I dedicate to my job."

He said his family and associates have been "injured" by the "screaming headlines in the press." He said he has wondered, "Did I have the right to put them through it?" But he has never had "a thought of resignation. No."

He said that the investigations have not kept the Labor Department from doing its job. "I assure you that we are second to no department in our contribution to the budget cuts, and to our attention to deregulation, with one aim in mind: to create jobs, jobs, jobs . . . . "

On the troubled economy, Donovan said he believes the Reagan economic program is working. He said that in August the unemployment figures held steady while "interest rates have begun to drop further, we are winning the battle against inflation, the stock market -- and that's a pretty good barometer . . . -- has had a tremendous revival.

"Which tells me that the American people see a growth and prosperity, and that's the message I would like to give to the American working man and woman, to please have hope."