The rematch between world chess champion Gary Kasparov and ex-champion Anatoly Karpov will begin sometime between July 28 and Aug. 4, the International Chess Federation (FIDE) announced yesterday.

Both players were present at the FIDE press conference at its headquarters in Lucerne, Switzerland, and both told reporters they were happy over the arrangement, which ended a long dispute over the timing of the rematch.

Still to be settled is whether the match will be played in London, Leningrad or both cities.

The British and Soviet chess federations have submitted competitive bids for the match. Kasparov and Karpov have both said they would prefer to play in Leningrad. But the announcement noted a resolution of the 1985 FIDE Congress that world championships should be held in different countries.

In view of this resolution, FIDE President Florencio Campomanes said, there have been some negotiations about starting the match in London and ending it in Leningrad. "FIDE considered, however, that it would be a better match if held in one place, therefore it could be entirely in London," he said.

The announcement, confirming unofficial reports circulating recently in the Soviet Union, ended the suspense about whether Kasparov might forfeit the title he had won less than three months ago.

Under the terms originally set up by FIDE, the defeated champion had the right to demand a return match beginning in February. But Kasparov refused, insisting that it was too soon after their last match, which he won in November.

"I was and am against the idea of a rematch in principle," Kasparov said yesterday, "but we managed to find a compromise to satisfy our mutual interests."

The exact date of the first game in the return match will be settled when its location is determined.

If the match is played in more than one city (a practice for which there are precedents in the history of the world championship), there could be inequity in the distribution of games. Like the last Kasparov-Karpov match, this one will be limited to 24 games, but there is no way of assuring that all 24 will be played. The winner will be the first player to win six games, so theoretically, the match could be ended within the first dozen games played in London.

The last match went to the limit of 24 games, with Kasparov winning by a score of 13 to 11. If the next match also goes the full distance, it is likely that the most intense interest will be in the final games played in Leningrad.