Labor Secretary Raymond J. Donovan said yesterday that he has no intention of resigning from President Reagan's Cabinet and denounced what he called "the relentless and cowardly attacks" that have been made on him and his New Jersey construction company.

Breaking a six-month silence about a stream of allegations linking him and his firm to organized-crime figures, Donovan said he expected the investigation of special prosecutor Leon Silverman to be completed "in just a few days" and he seemed confident that Silverman's report would vindicate him.

But meanwhile, Donovan protested, he has been victimized by a "presumption of guilt" that he said was particularly disturbing.

"Quite obviously," he said in a statement that he read to reporters at the Labor Department, "some of our elected officials are not content to allow facts to be determined in an orderly manner. They seem more interested in a wonderland school of justice that stands for judgment now, trial later."

The secretary did not name the "elected officials" he had in mind, but Senate Democrats last week publicly urged President Reagan to ask Donovan to "step aside" until all the allegations against him have been satisfactorily resolved.

The Democratic stand came on the heels of a disclosure that the incoming Reagan White House had been informed by the FBI on Jan. 12, 1981, the first day of Donovan's Senate confirmation hearings, that Donovan had "close personal and business ties with known La Cosa Nostra figures."

The Senate Labor Committee voted for his confirmation after a stormy set of hearings, but its leading members have since expressed concern over a number of allegations and reports of informants and organized-crime-case witnesses that the FBI did not bring to the senators' attention at the time.

Donovan said he hoped Silverman's report would be made public by the special panel of federal judges to whom it will be submitted under the Ethics in Government Act. Then, he said, "we may all examine in detail not only who has made charges, but their credibility, their motivations and the source of their knowledge."

Once the report is issued, Donovan added, "I shall have a great deal more to say about the many and vicious attacks that have been made upon me, my company and its employes." His company is the Schiavone Construction Co. of Secaucus, N.J.

Senate Labor Committee Chairman Orrin G. Hatch (R-Utah) has pledged a formal inquiry into the role of the FBI and the incoming Reagan White House in checking out Donovan's background, and said he is awaiting Silverman's report before undertaking that investigation. Donovan said he would be happy to testify if hearings are held, but added that he would also voice his concern "over the cavalier manner in which raw and unsubstantiated data has been leaked in total disregard for the rights of American citizens."

"When I came to Washington, 18 months ago," he continued, "I was quickly made aware of the old bromide that 'politics ain't beanbag.' I would, however, be less than honest--and human--if I did not state publicly my disgust with the relentless and cowardly attacks that have been made on me and my company by an alliance of individuals who have a total disregard for the truth."

Just back from a week-long work-vacation trip to Europe, Donovan said he and Schiavone Construction "have cooperated completely" in Silverman's investigation and that the special prosecutor has "had unrestricted access to company records as well as the private records of my associates and my family."

Donovan also noted that he pledged six months ago that he "would not comment" on the matters under investigation by Silverman and although "it has been extremely difficult . . . I have kept that pledge."

In concluding his statement, Donovan emphasized that "I have every intention of serving as secretary of labor and completing the job I was asked to do." The delivery was a slight departure from his prepared text, which said that he would stay "so long as I can be of service to President Reagan."

At the White House, deputy press secretary Larry Speakes brushed aside reports that some of Reagan's principal advisers think Donovan ought to step aside. He also dismissed reports that a list of potential successors has been drawn up as "bunk. There is no list."

In the Senate, by contrast, Minority Leader Robert C. Byrd (D-W.Va.) renewed his call for Donovan to step aside and expressed his concern about a report in yesterday's Washington Post. The report dealt with an allegation that an FBI informant last year provided the bureau with an assertion that Schiavone was "mobbed up" through one of Donovan's associates--but that was omitted from the documents provided to the Senate Labor Committee.

"If these articles are accurate," Byrd said in a Senate speech, "then the Senate as an institution, and the country, have been done a terrible disservice. To put it most succinctly, the Senate has been obstructed in the proper discharge of its constitutional responsibilities . . . to 'consent' to the appointment of 'officers of the United States' such as Mr. Donovan."

Declaring that his concern "goes far beyond the Donovan case," Byrd said he would offer legislation to "ensure that all relevant information bearing upon a nominee's fitness and qualifications for high government office is obtained and transmitted to the Senate prior to confirmation. Additional steps might also be necessary to affix clearly the responsibility and accountability of particular executive officers of our government to ensure that such information is not withheld."

A spokesman for Senate Majority Leader Howard H. Baker Jr. (R-Tenn.) said Baker was also concerned about "the prerogatives of the Senate as they relate to" the Donovan case and was trying to arrange a meeting with senior administration officials so that Baker and Byrd could "explore the situation."