NEW YORK (AP) _ A ragtag group of Vietnam veterans dubbed ''The Lost Patrol'' arrived Saturday at Grant's Tomb after a 269-mile march from Washington for a vigil for 2,400 Americans still missing in Southeast Asia.

Less than three dozen veterans made the full march, and only about 100 people greeted them upon their arrival in Manhattan - far below the 1,000 organizers had hoped to draw.

''There's only a small amount of us who care, but we do care, and we care a lot,'' said Anthony Torres, march organizer for the New York-New Jersey POW- MIA committee. ''People saw us marching. Truck drivers saw us. This is about public awareness.''

Outside the huge monument, the marchers and their supporters gathered in sweltering heat a half-block from a row of tents where many planned to stay in a 24-hour vigil.

They expressed a mixture of frustration and hope that prisoners of war and missing in action left in Vietnam would eventually be returned to U.S. soil.

Vietnam, which has cooperated for more than a year in the return of MIA remains, has repeatedly denied that it is holding prisoners, but their position leaves open the possibility that some live Americans remain behind.

Pentagon officials admit that some U.S. deserters still may be living in Southeast Asia.

The Reagan administration's official position is that the possibility of live prisoners cannot be ruled out. However, Pentagon officials speaking on condition of anonymity, say they have no credible reports of any prisoners.

Lou Ortega, a veteran of World War II, Korea and Vietnam, angrily called for the government to close the book on Vietnam by providing answers about the missing men.

''We served. Now ... serve us,'' he said. ''Give us an accounting of our POWs; give us an accounting of our MIAs. In that way, the stigma of this war will be finally removed.''

A huge banner proclaimed ''Release Our POW-MIAs'' behind the speaker stand on the monument steps. In the crowd, combat fatigues mixed with dress blues as the veterans opened their vigil with ''The Star Spangled Banner'' and a prayer before a lone bugler played taps.

A walkway outside the tomb was lined with plain white crosses with the home states and cities of the missing soldiers. An American flag hung just before the plaza outside the monument.

The rally followed a weeklong march that started at the Vietnam War Memorial in Washington, D.C., snaked through Delaware and New Jersey, and ended with the marchers crossing the George Washington Bridge into Manhattan.

The marchers were mostly from New Jersey and Texas, and had participated in a similar march in November from Dallas to San Antonio, Texas.