More than 200 Ukrainian Americans and their supporters picketed in the rain yesterday at McPherson Square, two blocks from the White House, to protest the U.S. government's treatment of Miroslav Medvid, a Soviet seaman who twice jumped ship in Louisiana in an apparent attempt to defect and both times was returned by U.S. immigration officials.

"Most of the people here are Republicans and voted for President Reagan," said Helen Danchenko, a Ukrainian language teacher. "They're very disappointed that this happened under this administration."

The peaceful demonstrators carried candles and signs with slogans that included, "Give Medvid asylum, send U.S. bureaucrats to an asylum," and "Mr. President, please help." They chanted slogans such as, "Hell, no, he won't go."

Medvid, 22, who speaks no English, twice jumped into the Mississippi River on Oct. 24 and twice was returned by border patrol officers, who did not understand his language. Four days later, Medvid, accompanied by Soviet observers, was removed from the freighter, Marshal Konev, and interviewed by State Department officials. They allowed his final return after he signed a Russian-language statement that he did not want to defect.

Since then, Irene Padoch, a translator who interviewed Medvid by telephone the day he jumped ship, said Medvid wanted to remain in the United States.

State Department officials said they consider the matter closed. But immigration officials' handling of the case has drawn criticism from Congress and prompted a Justice Department investigation.

Demonstrators at yesterday's rally -- organized by a loose coalition of Ukrainian-Americans and other Eastern European emigre groups -- said they believe the administration is fearful of insulting Soviet officials in the Medvid matter because of the upcoming Geneva summit.

U.S. officials "don't want to stir things up because of summitry," said Irene Kost, who helped organize the rally.

Planning for the protest began Friday, and word was spread to the Washington area's approximately 2,000 Ukrainians, organizers said.

Last week, one group asked the U.S. District Court here for an injunction to stop the ship's departure, but the request was denied. An appeal is pending. Meanwhile, a protest group called Save the Oppressed People said it is organizing a flotilla to try to prevent the departure this week of the grain ship from Reserve, La.