This comes as Prime Minister John Howard handed in his sworn statement about the scandal to the Cole inquiry.
In a written statement released to coincide with his appearance, Mr Downer said he did not know the kickbacks were being paid through a Jordanian trucking company, Alia, which was partly owned by Saddam's regime.
"My recollection is that I did not know and was not otherwise aware at any time during the period from about 1999 to 2003 anything about Alia," he said.
Mr Downer said he did not know "that money paid by AWB to Alia or any other Jordanian trucking company was paid, whether advertently or inadvertently on the part of AWB, to the Iraqis."
In the witness box before the commissioner, former judge Terence Cole,
Mr Downer denied knowledge of 21 diplomatic cables which were sent to his office warning about possible problems with AWB's practices in Iraq.
He said the cables had been assessed by his office and many were not thought worthy of bringing to his attention.
In his written statement, Mr Downer used the phrase "I do not have a specific recollection of having received or read this cable or of it otherwise being brought my attention" 19 times in relation to the 21 diplomatic cables.
He repeated the phrase with slight variations more than 30 times while testifying on the stand, admitting "no one's memory is perfect".
Mr Downer defended his department's failure to investigate warning signs that
AWB was paying kickbacks, saying he believed that the United Nations was vetting the contracts and that his department did not have the power or expertise to act.
Mr Downer, the second government minister to appear at the Cole inquiry probing the graft allegations, said he did not recall being told by former AWB managing director Andrew Lindberg last March that the trucking company Alia was part-owned by the Iraqi government.
The inquiry, headed by former judge Terence Cole, is looking into claims that AWB paid $220 million to Saddam's government to secure grain contracts worth more than $2.3 billion between 1997 and 2003 under the United Nation's oil-for-food program.
Earlier on Tuesday, Mr Lindberg told the inquiry he distinctly remembered a March 2005 telephone call in which he told Mr Downer details about Alia's ownership, and that money AWB paid to it might have found its way back to Saddam's regime.
Mr Lindberg said he informed Mr Downer that the UN investigation into corruption of its oil-for-food program was looking at Alia, and that money paid to it could have ended up in Saddam's coffers.
But Mr Downer said while he only had a "very distant recollection" of the conversation, he did not believe Mr Lindberg mentioned anything about Alia.
Instead, he said the first time he learned about Alia's name was in April 2005 and again in June during a meeting with Mr Lindberg in Canberra.
"If you had learned it on that day (in March 2005) would it be the first time you learned (about Alia)?" senior counsel assisting the inquiry John Agius SC asked.
Mr Downer replied: "I suppose it would have and .... if I had been told that I would have transmitted that information to someone else or made a note of it."
"Did you?" Mr Agius asked.
"No, I don't think I did," Mr Downer said.
"I'm pretty sure I didn't make a note of it."
The inquiry on Monday heard evidence from Deputy Prime Minister Mark Vaile.
Howard's statement
Senior counsel assisting the inquiry, John Agius, SC, said the inquiry's legal team had received Mr Howard's statement on Tuesday, and is tendering it as a confidential exhibit.
But lawyers for AWB and its executives could now read the document overnight and decide if they wanted to cross-examine Mr Howard at the inquiry.
"Overnight, I would ask my learned friends to consider whether they wish to make applications to examine the prime minister," Mr Agius said.
"We would return to the hearings on Thursday if necessary."
Mr Agius on Monday said he would read Mr Howard's statement before he decided whether to question him at the inquiry.