Joseph Paul Franklin, convicted two weeks ago of two racial killings in Salt Lake City, was charged yesterday with double murders in Oklahoma and Indiana, and federal authorities say he is the prime suspect in last year's shooting of civil rights leader Vernon Jordan in Fort Wayne, Ind.

The twin charges in Oklahoma City and Indianapolis appear to be an effort to get Franklin to confess in a series of racial murders. He faces sentencing in Salt Lake City on Monday for his conviction on federal civil rights charges, and Utah authorities plan to try him on state murder charges.

Oklahoma, Indiana and Utah all allow the death penalty for murder convictions.

Officials said yesterday it is possible that the 30-year-old drifter eventually will be charged with five additional racial killings, in addition to the Jordan shooting.

Steve Goldsmith, the Indianapolis prosecutor, said last night that federal authorities asked him to file the charges based on testimony by a cellmate who said Franklin boasted of the slayings of two black Indianapolis men in separate incidents in January 1980.

Asked if the multiple charges were an attempt to put pressure on Franklin, Goldsmith said, "One could draw that conclusion."

Franklin's name was first raised in connection with the Jordan shooting last fall after Salt Lake City police said he was wanted for questioning in the August sniper slayings of two black men, Ted Fields and David Martin, who were jogging with two white women.

FBI Director William H. Webster said after Franklin's arrest in October that he thought the wave of racial killings would cease. The FBI said then, though, that it had no real evidence to link him to the sniper attack on Jordan last May as the president of the National Urban League stepped out of a car driven by a white woman who was a member of the organization's Fort Wayne board of directors.

Webster told The Washington Post last month that Franklin had not been eliminated as a suspect in the Jordan case, and added, "I don't think he's going to be, either."

Officials yesterday refused to say specifically what new evidence they had tying Franklin to the attack on Jordan. But there were indications that Franklin had boasted to cellmates of several sniper attacks on blacks and that the FBI and authorities in several cities were zeroing in on evidence that placed Franklin at the shooting scenes.

For instance, Bill Lewis, an Oklahoma City homicide detective, said yesterday that "Franklin told friends and some of his cellmates that he, in fact, committed the homicides here in Oklahoma City and he told them specific details about the homicides."

Lewis said police also had established that Franklin was in the city at the time Jessie Taylor, 42, and his common-law wife, Marion Bresette, 31, were killed as they left a supermarket on Oct. 21, 1979.

The lead on Franklin's boasting was passed on by the Justice Department to Oklahoma City authorities after Franklin's conviction in the Salt Lake city trial, Lewis said. In that case, federal prosecutors admitted they didn't have a murder weapon or a witness, but depended on the testimony of several persons, including Franklin's ex-wife and two cellmates, who said he had told them about the killings of Fields and Martin.

Franklin denied that he committed the killings, but said the two men deserved to die because of "race-mixing."

Sources said Franklin is also the prime suspect in the murders of a 22-year-old black man and 16-year-old white girl as they were walking across a bridge in Johnstown, Pa., last June; the slayings a week earlier in Cincinnati of two black teen-agers, and the murder of another black man in Doraville, Ga., in 1979.