REYKJAVIK — Bobby Fischer, the reclusive chess genius who became a Cold War hero by dethroning the Soviet world champion in 1972 and later renounced his American citizenship, has died. He was 64.

Fisher died in a Reykjavik hospital yesterday, his spokesman, Gardar Sverrisson, said today. Icelandic media reported that he died of kidney failure after a long illness.

Born in Chicago and raised in Brooklyn, Fischer was wanted in America for playing a 1992 rematch against Boris Spassky in Yugoslavia in defiance of international sanctions. In 2005, he moved to Iceland, a chess-mad nation and site of his greatest triumph.

The former Russian chess champion, Garry Kasparov, said Fischer’s ascent in the chess world in the 1960s and his promotion of chess worldwide was “a revolutionary breakthrough” for the game. But Fischer’s reputation as a genius of chess was eclipsed, in the eyes of many, by his idiosyncrasies.

“The tragedy is that he left this world too early, and his extravagant life and scandalous statements did not contribute to the popularity of chess,” Kasparov said.

He lost his world title in 1975 after refusing to defend it against Anatoly Karpov. He dropped out of competitive chess and largely out of view, emerging occasionally to make erratic and often anti-Semitic comments, although his mother was Jewish.

Mr. Spassky said in a brief phone call from his home in France that he was “very sorry” to hear of the death of his friend and rival.

An American chess champion at 14 and a grand master at 15, Fischer dethroned Mr. Spassky in 1972 in a series of games in Iceland’s capital, Reykjavik, to become the first officially recognized world champion born in America.

The president of the World Chess Federation, Kirsan Ilyumzhinov, called Fischer “a phenomenon and an epoch in chess history, and an intellectual giant I would rank next to Newton and Einstein.”

The match, at the height of the Cold War, took on mythic dimensions as a clash between the world’s two superpowers.

Fischer played — and won — an exhibition rematch against Mr. Spassky on the resort island of Sveti Stefan, but the game was in violation of American sanctions imposed to punish then-President Slobodan Milosevic.

In July 2004, Fischer was arrested at Japan’s Narita airport for traveling on a revoked American passport and threatened with extradition to America. He spent nine months in custody before the dispute was resolved when Iceland granted him citizenship and he moved there with his longtime companion, the Japanese chess player Miyoko Watai. She survives him.

In his final years, Fischer railed against the chess establishment, alleging that the outcomes of many top-level chess matches were decided in advance.

Instead, he championed his concept of random chess, in which pieces are shuffled at the beginning of each match in a bid to reinvigorate the game.

“I don’t play the old chess,” he told reporters when he arrived in Iceland in 2005. “But obviously if I did, I would be the best.”

Born in Chicago in March 9, 1943, Robert James Fischer was a child prodigy, playing competitively from the age of 8.

At 13, he became the youngest player to win the United States Junior Championship. At 14, he won the United States Open Championship for the first of eight times.

At 15, he gained the title of international grand master, the youngest person to hold the title.

Tall, charismatic, and with striking looks, he was a chess star — but already gaining a reputation for volatile behavior.

He turned up late for tournaments, walked out of matches, refused to play unless the lighting suited him and was intolerant of photographers and cartoonists. He was convinced of his own superiority and called the Soviets “Commie cheats.”

His behavior often unsettled opponents — to Fischer’s advantage.

This was seen most famously in the showdown with Mr. Spassky in Reykjavik between July and September 1972. Having agreed to play Mr. Spassky in Yugoslavia, Fischer raised one objection after another to the arrangements and they wound up playing in Iceland.

When play got under way, days late, Fischer lost the first game with an elementary blunder after discovering that television cameras he had reluctantly accepted were not unseen and unheard, but right behind the players’ chairs.

He boycotted the second game and the referee awarded the point to Mr. Spassky, putting the Russian ahead 2-0.

But then Mr. Spassky agreed to Fischer’s demand that the games be played in a back room away from cameras. Fischer went on to beat Mr. Spassky, 12.5 points to 8.5 points in 21 games.

Americans, gripped in their millions by the contest, rejoiced in the victory over their Cold War adversary.

In the recent book “White King and Red Queen,” the British author, Daniel Johnson, said the match was “an abstract antagonism on an abstract battleground using abstract weapons … yet their struggle embraced all human life.”

“In Spassky’s submission to his fate and Fischer’s fierce exultant triumph, the Cold War’s denouement was already foreshadowed.”

The victory made Fischer the first American-born world champion. Paul Morphy, an American, was regarded as the world’s best player from 1858 to 1862, and William Steinetz, an Austrian immigrant to the United States, was an official champion from 1886 to 1894.