WASHINGTON (AP) _ Three Supreme Court justices turned down an application to prevent the Soviet freighter with Miroslav Medvid aboard from leaving the United States, a court spokeswoman said Saturday night.

Medvid was forced back onto the vessel, the Marshal Koniev, after jumping ship Oct. 24. The seaman also jumped a second time, from a ship returning him to the freighter. The State Department he later changed his mind and said he wanted to return to the Soviet Union.

The application, which had been denied by the 5th U.S. Circuit Court of Appeals in New Orleans, was presented to Justice Byron White at 6:20 p.m. and White denied it half an hour later, said court spokeswoman Toni House.

The petitioners, who said they were an aunt and cousins of Medvid, then turned to Justice William Brennan, who rejected their petition at 7 p.m., she said.

The petitioners then sought to go to Justice Thurgood Marshall, who was unavailable, so they sought help from Justice Lewis Powell. Justice Powell's rejection followed at 8 p.m.

Paul Kamenar, a lawyer for the petitioners, said after the third rejection: ''I think it's futile now. The ship gets further away.''

He had filed a petition for a writ of habeas corpus, which is a court order to produce someone being held for an examination to determine whether the detention is lawful. He asked that the writ be directed to the captain of the Marshal Koniev and the Customs Service. No reasons for the rejections where given at any stage, he said.

According to Kamenar, the petitioners were Mary Filipovic, from Wadsworth, Ohio near Cleveland, who he said was Medvid's aunt; Ann Kent, who he said was a cousin, and her mother, Paraska Jeziersky. They were joined by Sens. Gordon Humphrey, R-N.H., and Charles E. Grassley, R-Iowa, and Rep. Robert L. Livingston, R-La.