"There will be no deportation today," an immigration bureau official told the Mainichi Daily News. However, he refused to rule out future action.
Earlier Tuesday, Justice Minister Daizo Nozawa rejected Fischer's application for refugee status and dismissed his appeal against a deportation order.
Fischer's lawyers, Takeshi Ohashi and Masako Suzuki, said in a joint statement Fischer believes he is being persecuted by immigration officials.
"We must strongly object to the immigration bureau's reactions," the lawyers said.
The former chess champion is wanted by the United States for traveling to Yugoslavia for an exhibition game in 1992, thereby breaking U.N. sanctions on the country.
A U.S. State Department spokesman said a U.S. consular officer would visit Fischer "soon" but refused to comment further.