The challenge came after the Senate committee investigating the claims warned the MP that he could face prosecution over "false and misleading statements under oath" he allegedly made while giving testimony in Washington five months ago.
The committee said it had traced proceeds of $150,000 (£85,000) from Iraqi oil sales in a bank account of Mr Galloway's estranged wife, Dr Amineh Abu-Zayyad, and that another $446,000 was given to the Mariam Appeal, a leukaemia charity run by the MP. Mr Galloway said the committee chairman, Republican senator Norm Coleman, was carrying out "sneak revenge attacks" in response to the "humiliation" suffered when the MP appeared in Washington.
Mr Galloway, the Respect Party MP for Bethnal Green and Bow, may, however, face investigations by three authorities in this country.
The Foreign Office has said the allegations have been drawn to the attention of "relevant authorities".
They are believed to be the Charity Commission, which inquired into the Mariam Appeal last year; the Parliamentary Commission for Standards, which can examine if Mr Galloway broke any of its rules; and Customs and Excise, which can investigate whether sanctions imposed on Iraq were breached.
Interest will also be focused on the next report by UN investigators, due out later this week, which is expected to name companies that had illegally benefited from oil-for-food.
The Senate committee claims that Fawaz Zureikat, a Jordanian friend of Mr Galloway, channelled the money from the Saddam regime to the Mariam Appeal and the MP's wife.
However, The Independent has learnt that despite the apparent severity of the charge, Mr Zureikat is still trading in Iraq and has made business trips to the US with the approval of American authorities.
Mr Zureikat told The Independent: "I have been to Washington, New York and Texas travelling on my own passport with the knowledge of American officials. No one wanted to question me. I have re-started my business with Iraq and I have an office there. Iraqi officials have encouraged me to continue doing business.
"I have had meetings with American officials. They wanted to talk to me about Iraq before the war, but oil did not come up and George Galloway did not come up. I asked them to check me out and they said they had done that and there were no problems."
He said he was still sending money to the family of Mariam Hamza, the leukaemia sufferer after whom the charity was named, but "this had nothing to do with oil sales".
Mr Galloway told the Senate committee yesterday: "Please, please charge me, please prosecute me and I will be on the next plane to America to see you in court.
"I am demanding prosecution. I am begging for prosecution. If I have lied under oath in front of the Senate, that's a criminal offence. Charge me and I will ... face them down in court as I faced them down in the Senate room."
Mr Galloway said he did not wish to answer for his wife. The Senate report quotes a written reply from Dr Abu-Zayyad, saying: "I have never solicited or received from Iraq or anyone else any proceeds of any oil deals, either for myself or for my former husband."
Mr Galloway said: "The [Senate] documents do not say any money went into my bank account. I have never benefited from any oil deal and I have never asked anyone to act on my behalf."
The Senate committee said its information had come from interviews with former figures in Saddam's regime such as deputy prime minister Tariq Aziz and vice-president Taha Yasin Ramadan.
Mr Galloway said: "The evidence is statements made by people on trial for genocide and now living in the dungeons of the American occupation in Iraq. Knowing what we do about what happens to people in those dungeons, you don't have to be a genius to work out why, after May, they would get somebody to say what they want them to say."
The oil-for-food programme inquiry has resulted in charges being filed in the US and France. Two former French officials, Serge Boidevaix, an ex-director of the foreign ministry, and Jean-Bernard Merimee, a former ambassador to the UN, are facing corruption charges.
In the US, executives from Midway Trading Company have pleaded guilty to charges of grand larceny.
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