The Telegraph has discovered that Mr Fischer gave an interview to an obscure radio station in the Philippines hours after the events on September 11.
Mr Fischer is already wanted for questioning by the FBI for breaking UN sanctions by taking part in a chess match in Serbia against Boris Spassky in 1992 - his first for 20 years.
In his interview on September 11 with Radio Bombo in Baguio City, Mr Fischer said: "This is all wonderful news. It is time to finish off the US once and for all.
"I was happy and could not believe what was happening. All the crimes the US has committed in the world. This just shows, what goes around comes around, even to the US.
"I applaud the act. The US and Israel have been slaughtering the Palestinians for years. Now it is coming back at the US."
Mr Fischer, 58, also attacked Israel and "Jews" who he claimed were responsible for "bringing" the attack on the World Trade Centre. He gave the interview because he is a friend of Pablo Mercado, the station manager. They met through their mutual friend Eugene Torre, the Filipino chess grandmaster.
Last night Mr Mercado confirmed that he took the call from Mr Fischer and then interviewed him live on air. He has met Mr Fischer on several previous occasions with Mr Torre.
Mr Mercado said: "Bobby rang me up while he was watching the events in New York live on television. He felt so strongly about what he was watching, he wanted to say the American government had it coming to them.
"I was shocked but not surprised. I know his views about America because I have spoken to him on a number of occasions and met him through our mutual friend Eugene Torre. It is Bobby Fischer without a shadow of a doubt."
Mr Mercado said that Mr Fischer had put on weight since his last public appearance and talked constantly of his old chess matches. He always carried chess books with him.
The Telegraph tracked down Mr Fischer to his hideaway in Japan on Friday but he put the telephone down. Mr Fischer, who has been a grandmaster since the 1950s, became the first - and so far only - American world champion in 1972.
He disappeared for the best part of 20 years before surfacing in 1992 to play against his old opponent Spassky for $5 million.
The match broke sanctions imposed by the United Nations and in a controversial move he was indicted in the United States. President George Bush, the father of the current president, gave his personal approval for the legal action.
Mr Fischer, who usually lives in Hungary, is a well-known anti-Semite who has spoken out against "the international Jewish conspiracy".