'Whether he wins any prize money or not, by his going there he will be in violation of our regulations pursuant to trading with the enemy,' said Bob Levine, a spokesman for the department.
'The people at the foreign actions control take this very seriously,' he said. Fischer's lawyers have been notified of the probability of a court action and a possible penalty of dollars 250,000 ( pounds 126,000) and/or 10 years in prison.
Fischer, 49, who withdrew from competition after winning the world championship in 1972, is due to begin a replay of that title match against Boris Spassky on the island of Sveti Stefan, in Montenegro, next Wednesday. The second half of the match will be played in Belgrade. Jezdimir Vasiljevic, a Serbian banker, has put up a dollars 5m ( pounds 2.5m) prize fund to lure Fischer out of retirement.
After being quoted as describing the event as 'open war' against United Nations sanctions, Mr Vasiljevic later denied that the match had anything to do with politics. 'This is a pure, private, show-business spectacle,' he said.
In a brilliant career punctuated by withdrawals from matches and tournaments, Fischer had mixed relations with the US authorities. In 1964, when denied a visa to visit Cuba, he played his games by telex from New York.
However, in 1972, when Fischer was threatening not to turn up for his world title challenge, it was widely reported that his decision to play was influenced by a telephone call from Henry Kissinger, exhorting him to play his part in defeating the commie menace.