Ukrainian-American groups, members of Congress and possible U.S. relatives of the Soviet sailor who twice jumped ship in Louisiana pressed urgently yesterday for a way to stop the ship from departing American waters until the mystery surrounding the sailor is resolved.

The Ukrainian groups petitioned the U.S. Court of Appeals here late yesterday to order the Immigration and Naturalization Service to block the departure of the Soviet freighter. A district court judge refused to issue such an order Friday.

The ship Marshal Konev, with the sailor, Miroslav Medvid, 22, on board, is anchored in the Mississippi River north of New Orleans awaiting a shipment of grain at Reserve, La. It is not expected to leave U.S. waters until next week.

Three Republican senators -- Gordon J. Humphrey (N.H.), William L. Armstrong (Colo.) and Rudy Boschwitz (Minn.) -- yesterday joined more than a dozen other members of Congress in a written appeal to President Reagan to take action to protect the sailor, who speaks no English.

The three suggested that Medvid be transferred to a "neutral third nation where he would be provided with an opportunity to recuperate, overcome any effects of drugs and regather his thoughts."

Democratic Reps. Donald J. Pease and Edward F. Feighan of Ohio informed the president that two of their constituents in suburban Cleveland say they think that Medvid might be a relative. The House members asked Reagan to hold the ship. "This could have a significant bearing on Mr. Medvid's decision," the two told the president in a telegram Friday.

Anne Kent of Strongsville and Mary Filipovic of Wadsworth told the congressmen that they think they are the sailor's second cousins and that their mother, Pareska Jeziersky of nearby Parma, is his great-aunt, an aide to Feighan said.

Medvid dived from his ship on Oct. 24 and swam ashore in Belle Chasse, La. He was interviewed by telephone by a translator, Irene Padoch, who said the sailor wanted to defect.

Border Patrol agents, however, decided Medvid was not seeking asylum and shuttled him back to the ship on Oct. 25. He jumped into the river again turning that trip.

Last week U.S. officials interviewed Medvid at length and he signed a statement saying he wanted to return home.