Two senior Democrats on the Senate Labor Committee yesterday urged a formal investigation of the FBI's performance last year in checking out the qualifications of Secretary of Labor Raymond J. Donovan.

Sen. Edward M. Kennedy (Mass.), the ranking minority member, and Sen. Thomas F. Eagleton (Mo.) made the request in separate letters to the committee chairman, Sen. Orrin G. Hatch (R-Utah).

Kennedy said he thought an inquiry was needed because of a "failure on the part of the FBI" to provide the committee with all the information at its disposal. Eagleton called for hearings into the role of both the FBI and White House counsel Fred Fielding, who was in charge of checking out high-level appointments for the Reagan administration.

Hatch did not rule such an investigation out, but he said through a spokesman that he was determined to wait until special prosecutor Leon Silverman completes his work.

Silverman was appointed in December under the Ethics in Government Act to investigate charges that Donovan was present at a 1977 luncheon when another executive of his New Jersey construction company made a $2,000 payoff to a labor union leader. A New York lawyer, Silverman has since expanded his inquiry into allegations that Donovan or his company had ties to organized crime as well as other issues that were unknown or unresolved at the time of Donovan's 1981 confirmation hearings.

The calls for a new look by the Senate Labor Committee came on the heels of disclosures that the FBI told Fielding on Jan. 11, 1981, the day before Donovan's first Senate hearing, of both a "tape recording" linking Donovan's name to "hoodlums" and of a separate allegation that Donovan had gone to Miami with a gangland figure for the 1979 Super Bowl weekend.

FBI executive assistant director Francis M. (Bud) Mullen said that he decided not to inform the committee that Donovan had been mentioned on an organized-crime wiretap. He said in an interview that he did not want to "open up that whole investigation" underlying the wiretap and defended his decision on the grounds that the conversation involving Donovan's name was "not pertinent."

According to informed sources, Silverman this year directed a crash program to transcribe all the tapes in question and discovered repeated references to "Ray" Donovan and to a number of other officials of his firm, the Schiavone Construction Co. of Secaucus, N.J.

In his letter to Hatch, Eagleton said he believed "very strongly that there are two basic issues in the Donovan case. One is Mr. Donovan's alleged 'mob' connections. The special prosecutor is properly pursuing that.

"The other is the question of the role of the FBI and Mr. Fred Fielding at the White House. Was the FBI fully forthcoming in its investigation? Did Mr. Fielding shield information from the FBI and/or the Labor and Human Resources Committee?

"Regardless of what the special prosecutor does or does not do, the . . . committee MUST investigate the latter questions."

Kennedy took a similar position, contending in his letter that the integrity of the Senate confirmation process was involved and that the committee should, "at a minimum, issue a report as to our findings and conclusions."

Aides to the two Democrats said they both want formal hearings.

Hatch said through his spokesman that he "is as concerned as Kennedy and Eagleton, but he feels he's got to wait until the special prosecutor comes forth with his report."

One source close to Mullen, who is now acting administrator at the Drug Enforcement Administration, suggested that he was taking an unfair beating for trying to protect an "extremely sensitive" organized-crime investigation.

This source said that the committee was apprised of "an awful lot of information about these allegations" last year, although not the fact of the extensive wiretap that might have been explored for further details.

Mullen, however, continued to endorse the results of the FBI's investigation in unusually strong terms. For instance, he assured the committee a few days before Donovan was confirmed that the bureau's inquiry had "surfaced no information which would reflect unfavorably upon Mr. Donovan in any manner."