The U.S. marshal for the District of Columbia, after just two weeks on the job, has become embroiled in a major confrontation with the Justice Department and marshal headquarters over who had the responsibility for transporting John W. Hinckley Jr. to court last week from St. Elizabeths Hospital.

The U.S. Marshal Service refused to confirm or deny reports from various knowledgeable sources that James O. Golden, who was sworn in as marshal on Aug. 2, may be considering retirement or resignation as a result of the disagreement.

The dispute over who was in charge of Hinckley's transportation came to a head last Monday when two sets of deputy marshals, one from headquarters and one from Golden's office, showed up at St. Elizabeths to claim custody of Hinckley. Hinckley eventually was transported to court without incident.

Sources said the dispute over Hinckley's custody was the latest in a series of disagreements between Golden and his superiors in the short time he has been U.S. marshal here.

It was confirmed yesterday that William E. Hall, the director of the U.S. Marshal Service, has asked Anthony J. Furka, a chief deputy U.S. marshal in the Washington office, to take over operations there as of yesterday. Furka, reached by telephone, refused to discuss Golden's status except to say, "I'm running the office for the time being."

Sources said the dispute last week apparently centered on Golden's assertion that his deputies in the Washington office had responsibility for bringing Hinckley to U.S. District Court for a hearing on Hinckley's mental status and commitment to St. Elizabeths. These sources said that despite Golden's claim of jurisdiction, the witness security section of the marshal service had standing orders from Attorney General William French Smith to transport Hinckley to the courthouse for the same Aug. 9 hearing.

The result was the two sets of deputy marshals that showed up at St. Elizabeths to pick up Hinckley, who has been confined there since June, after a jury found he was legally insane when he shot President Reagan.

A compromise was reached and a contingent of deputy marshals, half from the Washington office and half from headquarters, brought Hinckley to the courthouse, sources said.

The incident at St. Elizabeths was then brought to the attention of the Justice Department, where Golden met last week with associate attorney general Rudolph Giuliani, sources said. Justice had no comment late yesterday about Golden's status.

U.S. marshals are appointed by, and serve at the pleasure of, the president.

Golden, 57, had been director of the Enforcement Criminal Conspiracies division at the Law Enforcement Assistance Administration before he was nominated to be marshal by President Reagan. Golden replaced J. Jerome Bullock, 34, who held the job for five years after his nomination by then-president Jimmy Carter.

Reagan nominated Golden eight days after the Hinckley trial ended on June 21. The day after the jury's verdict, Hinckley was committed to St. Elizabeths and taken out of the custody of the marshal service. The question of his custody became complicated, however, when the time came to bring Hinckley to federal court for his Aug. 9 commitment hearing.

A Marine Corps veteran, Golden has an extensive background as an investigator, including six years as a special agent with the U.S. Secret Service and a year as director of security for the Hughes Tool Company in Las Vegas.