Special prosecutor Leon Silverman confirmed yesterday that he is investigating a new set of allegations against Labor Secretary Raymond J. Donovan and that he intends to stay on the job until he has run them down.

At the Labor Department, a spokesman said Donovan would have no comment on the unexpected reopening of the inquiry.

Appointed in December under the Ethics in Government Act, Silverman announced June 28 that there was "insufficient credible evidence" to prosecute Donovan on any charge despite a "disturbing number" of allegations that Donovan had been connected to reputed organized crime figures.

Donovan had roundly denied any such connections, both in testimony last year at his confirmation hearings before the Senate Labor and Human Resources Committee and this year before a federal grand jury sitting in Brooklyn under Silverman's direction.

Silverman said he had intended his June report to be a final one, but he still had some administrative chores to conclude and so did not write the required final notification letter to the attorney general, certifying that his work was finished.

Now, he said, "since additional allegations have come in and I am still in office, I feel an obligation to pursue them."

Silverman declined to discuss the nature of the charges, but sources indicated that some of them deal with new assertions of some kind of relationship between Donovan and a deceased New Jersey labor racketeer, Salvatore Briguglio.

These sources also indicated that there still appears to be little substance to the new reports although FBI agents working for Silverman are still pursuing them.

Among the allegations concerning Briguglio that Silverman has already explored are claims that Briguglio received payoffs from Donovan in the mid-1960s in return for inside information on public construction projects in the northern New Jersey area.

Donovan said he has never met Briguglio. A reputed Mafia hit man, Briguglio was a prime suspect in the 1975 disappearance and presumed murder of onetime Teamsters union boss Jimmy Hoffa when Briguglio himself was shot down on a New York street in 1978.

Silverman is also believed to be checking into reports that the name of Donovan's New Jersey construction company, Schiavone Construction, cropped up a number of times in the course of the FBI's investigation into the Hoffa case.

That was reportedly mentioned by FBI Director William H. Webster in a Dec. 12, 1980, telephone conversation with E. Pendleton James, then personnel chief for the Reagan transition team. Webster, it was understood, also advised James that there was nothing necessarily questionable about the fact that Donovan's company had been mentioned in the sweeping Hoffa investigation.

President Reagan nominated Donovan for the Cabinet post on Dec. 16, 1980, following a brief flurry of news reports indicating that the appointment had been derailed.

Silverman said he did not know how long his renewed inquiry would take, but emphasized that he does not intend to "stay in business forever."

He said, "We are checking all of the allegations that have been made since the June report was made" to the special panel of federal judges who appointed him. "Then we will write a supplemental report to the court and that will be the end of our activity, unless something turns up."