On the final stop of a highly publicized American tour, outspoken World Chess Champion Gary Kasparov yesterday blasted the leader of his native Soviet Union in a free-for-all question-and-answer session at Harvard's Russian Research Center.

For one hour at the center in Coolidge Hall, about 60 Soviet scholars and local chess enthusiasts shot. questions at Kasparov, who in 1985 became the youngest chess Grand master in history at age 22. Kasparov, a full member of the Soviet Communist Party since 1984 and a Azerbaijani Central Committee member, will play an exhibition chess match in Cambridge today.

"You must support change in the Soviet Union, but you cannot support the man who has now become a dictator," Kasparov said, in frankly-worded remarks about Soviet leader Mikhail S. Gorbachev.

An Armenian born in largely Muslim Azerbaijan, Kasparov touched on disparate topics ranging from Gorbachev to the Azerbaijani crisis to the Communist Party yesterday, displaying the iconoclasm that has made him a symbol for Soviets backing social change.

"I think it is entirely Moscow's fault that the conflict is not resolved yet," he said, speaking of the struggle between Azerbaijan and Christian Armenia. Kasparov said he doubted a quick solution can be found to religious and ethnic strife there that has killed hundreds, displaced approximately 100,000 and threatened to burst into civil war.

The chess master blamed much of the Soviet Union's problems on Gorbachev. Kasparov, a former backer, said he became disillusioned with the Soviet leader in February when it became clear to him "that Gorbachev only wants perestroika of the system, but the Soviet people want perestroika of the society."

Gorbachev's very popularity in the Westthreatens his proposed restructuring, Kasparovsaid. "With this blanket support for Gorbachev, itis very bad for perestroika itself."

Kasparov expressed hope that the Soviet Unionwould soon become a multi-party state.

"One thing we know for sure: communism doesn'twork," he said. "I think it is quite simple: weshoot for the Hungarian way," Kasparov said,referring to the East European nation's startlingdeclaration last week that it is becoming ademocracy.

The chess champion also said he wished to forma new political party in the Soviet Union to"destroy the Communist base in the country,slowly."

"Some people say that socialism must have ahuman face," he said. "To that phrase, my responseis that Frankenstein's [monster] had a human facetoo."

Kasparov originally joined the party "to avoidcomplications" so he could compete in chess, hesaid. Speaking of his friends now, he added, "Wedon't see any reason to leave it now; we believewe will be expelled quite soon."

In a lighter moment yesterday, Kasparov turnedto the chess-playing aspects of his visit. He willbe in Cambridge until Monday on the last stop ofan American tour that included visits to New Yorkand Washington, D.C., and appearances on nationaltelevision.

In New York, the man who has accumulated thehighest chess ranking ever twice beat "DeepThought," ballyhooed as the world's most powerfulchess-playing computer. Kasparov said that he didnot fear machines' entry into the chess world.

"It's very good for chess," he said, "althoughI hope the computer will never beat the worldchampion."

This afternoon, Kasparov will simultaneouslyplay six humans and two computers in a 1 p.m.exhibition match in Sanders Theatre. Playersinclude three Harvard chess team members--Vivek V.Rao '91-'92, Andie Serrota '91 and Issa N. Youssef'90--former U.S. women's champion AnnaAkhsharumova, Harvard visiting scholar Noam Elkiesand an IBM entrant.

Rao, a senior master, is the highest-rankingplayer at Harvard. He previously lost to Kasparovwith a team of players in 1987 in New York City.Harvard Chess Club President Daniel H. Edleman'91, who is not playing today, played Kasparov toa draw in a similar team effort on that tour.

"I hope I will win more games than I lose; Ihope I win more games than I draw," said Kasparov.

Although Harvard is the only universityKasparov is visiting, Rao said that "the fieldhere isn't as strong as it is in most places heplays.