"Renunciation does not allow a person to escape possible prosecution for crimes that they may have committed in the United States, or repayment of financial obligations previously incurred in the United States," department spokesman Tom Casey said, adding he could not provide any details about the case because Fischer had not signed a privacy waiver.
Fisher, a former world chess champion, is wanted by the United States for violating U.S. law in 1992 and playing chess in the former Yugoslavia, which was under an international travel ban.
He has lived in Japan ever since. His lawyer announced Monday that Fischer wanted to marry Miyoko Watai, the head of the Japan Chess Association. He also wants to renounce his U.S. citizenship.