Herman A. Sillas Jr., U.S. attorney for the eastern district of California, resigned today after being virtually invited to do so last Friday by White House counsel Lloyd Cutler.

Cutler issued a statement Friday saying that allegations that Sillas had taken a bribe from a southern California confidence man in 1974 remained "unproven." Cutler warned, however, that "the necessary relationship of mutual trust and confidence between the Department of Justice and Mr. Sillas has been impaired."

Cutler suggested Sillas "examine his position in light of these conclusions."

Today, Sillas read from a scrawled statement on yellow-lined paper that "I have this morning forwarded my resignation effective Oct. 1, 1980, to President Carter." Sillas said the prosecutor's job does not fit in with his freewheeling personality.

However, he flatly denied he had been forced out by nine-month-old charges that he had accepted a $7,500 bribe from a southern California confidence man named Richard Timothy Workman. Allegedly, Sillas had accepted the money prior to becomming director of the Department of Motor Vehicles in the administration of Gov. Edmund G. Brown Jr. in exchange for his promise to help Workman retain his license to run a used car lot in Fullerton.

Workman, now serving 13 years in a state prison in Chino on grand theft, fraud and other charges, took and passed three polygraph tests administered by the U.S. Justice Department. Sillas failed two similar tests.

But Sillas, 46, appointed chief federal law enforcement officer for 34 of California's 58 counties by President Carter in 1977, refused to resign.

After the bribe charges and an attendant attempt to force him out where disclosed, several Mexican-American groups rallied to his defense, threatening to work against Carter's reelection if Sillas was removed.

That left the White House with the unappetizing political choice of firing a popular Latino figure and possibility alienating Hispanic voters in a pivotal state in an election year, or not firing him and facing the wrath of Justice Department officials convinced of Sillas' guilt.

Then, on July 15, Sillas held an extraordinary news conference at the National Press Club in Washington to assert his innocence, say he was refusing a third lie detector test, and declare he was not going without a fight.

Two days later, a furious Michael E. Shaheen Jr., head of the Justice Department's Office of Professional Responsibility, held his own news conference to accuse President Carter of "inexcusable conduct" in keeping Sillas in office.

Cutler promised immediate action. In the ensuing month and a half, federal sources speculated that the Carter administration would come up with a compromise exactly like the one that appears to have been reached -- in exchange for Sillas' willing departure, the White House would say the charges were unproven.

But Sillas denied that. He said he had spoken to Cutler only once, last Friday when the White House counsel called to tell him that, in Sillas' words, he was cleared.

He did add, however, that he was unwilling to leave as long as the allegations were unresolved.

"I could not leave," he said. "I owed it to my family and myself and my supporters in the community that there would not be any cloud hanging over my head when I left.

"Whether I wanted to accept it or not, many people in the community view me in a model role and I did not want to set back that community in any way, I did not want anyone in any way to say, 'Well, you can't put in a Hispanic as a U.S. attorney.'"

Sillas also denied racism played any part in the investigation of him. Only the allegation that he was kept on because he is a Hispanic, he said, has racist overtones.