Gary Kasparov, the young chess maverick who Saturday became world champion, today offered an olive branch to his old foes in the chess establishment, saying he wanted to put past differences behind him.

"There is a big difference between a challenger and a champion," said the 22-year-old titleholder at a victory press conference today. "As challenger, I wanted . . . a fair game. As champion, I feel a big responsibility for the forthcoming cycle."

Kasparov appeared before several hundred journalists less than 24 hours after he stunned world champion Anatoly Karpov in the last game of their second championship match.

The youngest man ever to hold the crown, Kasparov was relaxed and animated, handling questions easily, sometimes with offhanded shrugs, at one point challenging journalists to a football match with chess players.

But despite the promise to let bygones be bygones, there was evidence of lingering strains between the outspoken new champion and some of the chess officials on the stage with him who sat unsmiling through his performance.

Karpov, 34, who had held the crown since 1975, was not at the press conference today, although he did attend a later crowning ceremony.

Kasparov today said his poor relations with the establishment could be traced to the end of his first match against Karpov but that now "all questions are fully in the past."

The new champion's first try at the crown was cut short in February when chess officials decided abruptly to end the grueling five- month chess battle. Kasparov and other chess experts took the decision, taken after Kasparov had scored two victories, to be a last-ditch effort to protect Karpov from defeat.

Kasparov today dodged questions about a rematch with Karpov, which under the recently amended rules of the last match would have to start by February. The two-year championship cycle has already begun and time has to be left for the regularly scheduled challenge match.

Kasparov has already complained about the rematch entitlement, saying it forces Karpov and himself into another match too quickly. He also noted that the new rule applies only to Karpov; as the new champion, Kasparov would not be entitled to a quick turnaround rematch were he to lose.

"It just turns into a competition between two men. We have played 72 games in the last eight months -- now in another two months; it just goes on and on," he said.

Karpov, who will head the Soviet Union's team at a tournament in Switzerland at the end of this week, has not said whether he will opt for a rematch, although one of his key advisors tonight said he is likely to.

Commenting on the championship match today, Kasparov said "the most pleasant moment" came in the 24th game when he moved in for the kill against Karpov. "There was a very interesting moment in the game when a dynamic balance was achieved when Karpov was forced to avoid a draw," he said.

Kasparov, who was ahead of Karpov 12 to 11, needed only a draw -- or one-half point -- to win the crown.

Kasparov today said he did not know what the prize money would be for the world championship, although the original rules set out that each player would get 80,000 rubles for each win and 16,000 for each draw.

Kasparov indicated that his reign would be different from Karpov's in at least some respects. Asked about Karpov's political activities, including chairing the Soviet peace fund, Kasparov said the former champion did things his way. For himself, he said, "I think all I can do for my country I have done."

Within the chess world, he said he did "not believe one man should decide the fate of chess. It should be all the grandmasters, together with the International Federation."

Privately, chess sources close to Kasparov indicated that some changes in the lineup of chess officials is likely in the near future, both in the Soviet and international organizations.