Alexander I. Solzhenitsyn, the dissident Russian writer living in Vermont, has refused an invitation to eat lunch at the White House today with President Reagan and a group of other former Soviet citizens.

The White House had invited Solzhenitsyn to join a group of Soviet dissidents in a symbolic demonstration of American solidarity with the dissident cause. Besides Reagan, the president's four top aides and Secretary of State Alexander M. Haig Jr. are scheduled to take part in the luncheon.

The White House had intended that Solzhenitsyn have a private, 15-minute meeting with Reagan before the lunch, but a letter to the writer outlining that proposal was never sent, and Solzhenitsyn decided that he did not want to join the group of other dissidents for lunch. According to a White House source, the letter proposing the meeting alone with Reagan was mislaid because of a bureaucratic foul-up.

Solzhenitsyn has informed the White House that he was displeased that news of the invitation appeared in the press before he received it, the source said. Moreover, Solzhenitsyn said, he did not think it was appropriate for him, a writer, to participate in what he described as a group of politicians and professional emigres.

When Solzhenitsyn first moved to this country in 1975, President Ford, on the advice of his secretary of state, Henry A. Kissinger, declined to meet with the writer, whose trilogy on Stalin's prison camps, "The Gulag Archipelago," had made him a symbol of internal opposition to the Soviet government. Reagan and his supporters attacked Ford bitterly for this snub.

The Reagan administration sought to make a symbolic gesture by finally getting Solzhenitsyn to the White House. But officials did not want to invite him by himself, apparently because Solzhenitsyn has become a deeply controversial figure among some Soviet emigres and Americans as a result of his outspoken political views.

Others invited for today's luncheon include former Red Army general Pyotr Grigorenko; Pavel Litvinov, who led a Red Square demonstration against the Soviet invasion of Czechoslovakia in 1968; Valery Chalidze, an early associate of physicist Andrei Sakharov in human rights activities; Andrei Siniavsky, a poet and philosopher now living in Paris; Mark Azbel, a longtime Jewish "refusednik" in Moscow who lives in Israel; Ludmilla Alekseyeva, a member of the original "Helsinki Watch Group" in Moscow; Georgi Vins, a Baptist preacher, and Aiche Ceitmuratova, a Crimean Tatar leader living in the United States.