Fischer, 61, also appealed a decision to deport him to the United States, where he has been wanted for defying sanctions on Yugoslavia by playing his former arch-rival Boris Spassky there in 1992.
The mercurial genius faces a possible fine or even a jail term if he is sent back to the United States.
A virulent anti-Semite, Fischer entered Japan in April and was detained at Tokyo's Narita airport July 13, traveling on what U.S. officials say was an invalid passport.
He was on his way to the Philippines.
Last week, Fischer filed a plea against deportation, which was rejected by Japanese immigration officials. Monday's second appeal was expected.
A decision could come later this week.
Supporters are said to be trying to obtain travel documents from a third country, possibly Germany, where his father was born, so that he could be flown there instead of the United States.