Teamsters union President Jackie Presser shattered a tradition yesterday by testifying voluntarily--if sketchily--before a Senate panel about a raft of allegations against him and his union, and by softening the union's opposition to a proposed anti-racketeering bill.

He also said that he has sent union auditors to investigate possible "hanky-panky" in some locals.

The 3 1/2 hours of questioning provided the first testimony by a Teamster leader on Capitol Hill in almost three years.

Presser, who took the union's top post six weeks ago, told skeptical members of the Labor Committee that he wants to change "the adversarial relationship" that has developed between the Teamsters and Congress, and asked that the senators judge him "on the basis of facts and actions, not on the basis of allegations by unnamed sources, insinuations and unsubstantiated assumptions."

Unlike his predecessor, Roy L. Williams, and other Teamsters officials, Presser appeared without being subpoenaed and did not exercise the Fifth Amendment protection against self-incrimination. He was, however, flanked by lawyers who advised him against answering questions concerning an ongoing federal investigation of a "ghost employes" scam in his home local in Cleveland.

Sen. Edward M. Kennedy (D-Mass.), whose brother Robert made history with his grilling of Teamster leader James R. Hoffa in the McClellan hearings of the 1950s, asked only two questions of Presser and left after about 30 minutes to attend another hearing.

The panel challenged Presser to make good on the promise he made when he took office of a "new day" for the Teamsters, with 1.8 million members the nation's largest union. The senators zeroed in on the Teamsters' infamous Local 560 in Union City, N.J., citing its reputation as a "captive" of the Provenzano family, whose members have been linked to organized crime and which has been plagued with murders, extortion and other felonious activities.

"It would seem to me that Local 560 is exactly the kind of local that should be investigated" by the international union, said committee Chairman Orrin G. Hatch (R-Utah), noting that "people who took on the Provenzanos have been getting murdered."

Presser repeatedly brandished a copy of the union constitution and, maintaining a soft, low voice, said he lacks the authority to throw people out of office without due process. "I am not a judge . . . ," he said. "This is not a dictatorial organization."

Presser's insistence on a written, signed request from a union member before he can investigate and order officials out of office seemed to frustrate the panel members.

"Isn't murder a pretty strong historical deterrent" against a union member's making such a written request, asked Sen. Sam Nunn (D-Ga.).

Nunn pressed the Teamster chief to tell whether it is possible for him to send an auditor to investigate the New Jersey local without the knowledge of Salvatore (Sammy Pro) Provenzano, an executive vice president of the Teamsters as well as an official of Local 560. Provenzano was among several local officials indicted recently on embezzlement charges.

Presser, after consulting with his attorneys, responded that he could do so and he added: "I've already assigned some into locals where I'm suspecting hanky-panky is going on."

Nunn continued to press him about investigating the New Jersey local. "Will you . . . ," Nunn began at one point. "Yes!" said Presser, cutting him off.

Presser drew praise as well as warnings from Hatch, who called his appearance a "marked departure" from the past, and his changed attitude toward the proposed anti-racketeering measure a "dramatic turnaround."

Presser said he accepts the principle of the bill, which would remove an official from union office upon conviction rather than allowing him to remain in office through the appeals process, as is now the case. But the Teamster chief said he objects to the provision's "double standard," which is stiffer for labor officials than for management.

The measure is expected on the Senate floor before the end of the month; two versions of the bill are before a House panel.

Hatch confronted Presser with a list of 48 Teamster officials convicted of violating federal labor racketeering statutes or other laws in the last three years who would be affected if the measure became law.