The U.S. Supreme Court yesterday cleared the way for the extradition to Israel of a 21-year-old Palestinian bombing suspect whose legal battle has become a rallying point for the American Arab community here.

The court denied a request that it review a U.S. Court of Appeals decision that found there was sufficient cause to believe that Ziad Abu Eain was involved in the May, 1979, bombing that killed two young boys and injured more than 36 civilians in the Israeli city of Tiberias. The Appeals Court also held that the bombing was not of a political nature and therefore Abu Eain was not exempt from U.S. extradition laws.

The decision on whether to grant Israel's extradition request now rests with Secretary of State Alexander M. Haig Jr. A State Department spokesman said yesterday that no decision has been reached. Seventeen Arab countries have already written Haig opposing the extradition request.

"The struggle will go on," said Ramsey Clark, a former U.S. attorney general who has acted as Abu Eain's attorney. "We will make an effort to have Israel withdraw its request and an effort to have Secretary Haig deny the request."

"If you want peace," Clark said, "you don't take sides in the internal political struggles of another country." Clark said Haig should deny the request as "the best public policy for peace."

A spokesman for the Israeli embassy here declined to comment on yesterday's ruling. The State Department has 60 days within which to make a decision, according to State Department attorney-adviser Frances A. Armstrong.

Abu Eain has been in prison for more than two years while his case has wound through the U.S. court system. The appeals court, in upholding a U.S. District Court magistrate's "probable cause" finding that there was sufficient evidence to charge Abu Eain with the crime, cited a statement of an alleged accomplice, who was since recanted.

The court also said that "indiscriminate bombing of a civilian populace is not recognized as a protected political act" and thus denied Abu Eain's contention that he was accused of a "political offense." The United States and Israel have an 18-year-old bilateral extradition treaty that covers such offenses as murder. The treaty exempts persons charged with an offense the U.S. considers of a "political character."

The case has sparked protests in the Arab community here. Dr. James Zogby, executive director of the American-Arab Anti-Discrimination Committee, said yesterday that Abu Eain's detention without bond for two years was "evidence that there in fact exists racism in this country against people of Arab descent . If he had been of any other descent it never would have happened."

However Jewish leaders claim that Abu Eain's extradition is justified. "The only real injustice in his case is that he has delayed his return to face trial in Israel for more than two years," wrote Washington attorney Nathan Lewin in a letter published recently in The Post.