LOS ANGELES (AP) _ Alleged Nazi war criminal Andrija Artukovic will appeal to another justice on the nation's highest court now that Supreme Court Justice William H. Rehnquist has refused to stop his extradition to Yugoslavia, his son says.

Rehnquist, in Washington, Tuesday night denied a request from lawyers for the 86-year-old man that he grant the stay while they filed an appeal of a 9th U.S. Circuit Court of Appeals decision against Artukovic.

In their ruling Tuesday, appeals Judges Harry Pregerson and Alex Kozinski said Artukovic should return to Yugoslavia to stand trial.

Artukovic's son, Rad, said he would ask his attorneys to take his father's appeal to another Supreme Court justice, but that the final authority belongs to Secretary of State George Shultz.

Assistant U.S. Attorney David Nimmer said Shultz would have the ultimate responsiblity for approving Artukovic's transfer to Yugoslavia.

Although Artukovic could be moved immediately, the government will not act until his last appeal is resolved, the prosecutor said.

The Supreme Court is the last possible stop on the long legal road to the extradition of Artukovic, whose case has been fought in U.S. courts for 36 years, said Nimmer.

Rad Artukovic blasted the Justice Department and judges for refusing to hear what he said was proof that testimony against his father was fabricated.

''I do know that they're trying to curry favor with the Yugoslavs and the price of good relations is my father's head,'' he said. ''I believe that the bargain has been consummated.''

Artukovic, legally blind and suffering from senility and heart problems, is imprisoned at the Federal Correctional Institution at Terminal Island. He has been in custody since November 1984 when his arrest by U.S. marshals reopened his case.

The government claims that Artukovic, interior minister in the Nazi puppet state of Croatia during World War II, was the notorious ''Butcher of the Balkans'' responsible for the deaths of 700,000 victims of Nazi atrocities.

Artukovic claims he is innocent and that affidavits submitted against him were perjured.

His lawyers say recollections of any surviving witnesses are false or so dimmed by time as to be unbelievable, and argue that their client can't get a fair trial in Yugoslavia.