The chairman of the Senate Labor Committee agreed yesterday to order another inquiry concerning Secretary of Labor Raymond J. Donovan in light of allegedly serious shortcomings in the FBI's investigation.

Democratic members of the committee, led by Sen. Edward M. Kennedy (Mass.), said in a letter delivered Friday evening to Chairman Orrin Hatch (R-Utah) that they had also come across another allegation involving Donovan's New Jersey construction company that "requires further investigation."

The Democrats suggested that Hatch call in the Fbi immediately, but he said he wanted committee investigators to come up with their own report first.

"All allegations, including these most recent ones, will be fully gone into and evaluated, in a thoroughly bipartisan manner, by the staff of the main Senate Labor Committee," Hatch said through a spokesman.

He said that any substantive findings would be immediately turned over "to the appropriate federal officials and law enforcement authorities."

Donovan said in a statement last night that he was not concerned by the renewed inquiry. He said he would concentrate instead on his duties as labor secretary. "I cannot allow myself to be distracted by scurrilous allegations," his statement said. ". . . I stand by my record."

The most serious of the new complaints raised by the Democrats involve two major shortcomings in the FBI investigation that were said to have been discovered by Bruce Locklin, a reporter with the Bergen, N.J., Record. Both dealt with allegations made by Ralph Picardo, a government-protected witness whom Donovan has denounced as "murdering slime."

One of the failings concerned a New Jersey contractor who allegedly served as a conduit of payments to organized crime figures for "labor peace" and who was said to have been a subcontractor for Donovan's company, Schiavone Construction Co.

In its report dated Jan. 23, the FBI said the businessman in question, Philip B. Moscato, has been reported to associate with organized crime elements."

But the FBI added that its Newark office "has no information indicating . . . any connection between him (Moscato) and SCC (Schiavone Construction Co.) or Mr. Donovan."

By contrast, reporter Locklin says he managed to contact Moscato directly and, the letter from committee Democrats continues, "Moscato acknowledged doing work for the Schiavone Construction Co." (Sources said that Locklin recorded the conversation with Moscato's permission. Locklin's account was scheduled to be published in the Bergen Record's Sunday editions.)

The other deficiency involves Armand Faugno, a reputed organized crime figure in New Jersey who disappeared years ago and is presumed dead. Picardo, who described himself as a bag man for payoffs by Donovan, told the FBI that Faugno was the one who initiated "the original extortion of SCC to keep labor peace."

Picardo had also told the Fbi that he picked up the payoffs from Donovan and from Schiavone Construction in the late 1960s as an employe of O.K. Trucking Co. Picardo said the firm was secretly owned by organized crime elements but operated by a man named Al Cecchi.

The FBI report noted that Cecchi, whom Picardo thought dead, was very much alive and, in an interview last month, called Picardo "a liar."

"He said he had no knowledge of any payments by SCC for 'labor peace' and . . . he advised . . . the name Armand Faugno was not familiar to him," the FBI reported.

FBI agents evidently did not carry that aspect of the inquiry any further.

However, reporter Locklin dug up an address book of Faugno's that had been provided to Locklin years earlier. Locklin reportedly found in it the name, address and phone number of Al Cecchi.

"Mr Locklin called the number, (and) reached Mr. Cecchi who admitted he did, in fact, know Mr. Faugno," the letter to Hatch stated. "Both of these (Locklin's) findings seemed to lend additional credence to the allegations of Ralph Picardo."

It was unclear why Cecchi might admit to a reporter what he denied to the FBI, but sources said Locklin drew the admission from Cecchi only after informing him his name, address and phone number were in Faugno's address book. ("Oh, you mean Armand Faugno," Cecchi was then said to have replied.)

The FBI took the position yesterday that "it would be premature for us to make any comment."

"We can't control what people say after they talk to us," an FBI spokesman said of Cecchi's reported admission. As for the apparent lack of knowledge about Moscato, he said: "If there are inaccuracies in our report, it could be incumbent on us to go back and clear them up. But until we see what's been said, it's premature for us to make any comment."

In his statement, Donovan expressed satisfaction with the FBI probe. "I was subjected to the closest, most thorough scrutiny since the confirmation of Nelson Rockefeller to be Vice President . . . I have a clear conscience."

In their letter to Hatch, Kennedy and his colleagues said they thought it important to get the FBI to investigate the allegations of still another government-protected witness, Patrick Kelly. Kelly recalled being told of ties between Schiavone Construction and members of the Genovese organized crime family.

Kennedy and his colleagues also called for an investigation of reports that Schiavone Construction "may have illegally purchased $30,000 cubic yards of top soil which had been obtained from public property."

The question goes back to a 1973 criminal trial involving the alleged misuse of public lands. The defendants, including one-time Hudson County, N.J., boss John Kenny, were acquitted.