New strategies are being assessed by the Iraq Study Group, formed in March at the urging of some members of congress to advise legislators and the US president on the war and alternative plans.
Pressure has been mounting on George Bush, the US president, for a change of direction in Iraq after the number of American soldiers killed reached 2,000 in October.
The daylight kidnapping of more than 70 employees of the ministry of education on Tuesday was the latest incident to demonstrate Iraq's deteriorating security situation.
"We should put responsibility for Iraq's future where it belongs - with the Iraqis"
Carl Levin, next chairman of senate armed services committee
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Senators from both parties seized on Abizaid's remarks as evidence that war managers had not identified a new, effective plan for Iraq.
Hillary Clinton, a New York Democrat, said: "Hope is not a strategy. I have heard over and over again the Iraqi government must do this, the Iraqi army must do that. Nobody disagrees with that. The brutal fact is, it is not happening."
Democrats have called for a new course in Iraq, and many are looking for an exit plan.
Carl Levin, the next chairman of the senate armed services committee, wants the Pentagon to start pulling troops out in four to six months.
"We should put the responsibility for Iraq's future squarely where it belongs, with the Iraqis," he said.
Meanwhile, a member of the Iraqi Baath party, speaking on condition of anonymity, told Al Jazeera on Wednesday that "US interference in Iraq" would not help the country move forward.
Abizaid told congressmen that US troop levels
in Iraq need to stay where they are
He said: "The Americans must stop interfering in Iraqi politics. They know what they have to do, so why aren't they doing it?
"US troops should leave Iraq. Only Iraqis can take responsibility for their own future, the Americans have no place in Iraq.
"The Americans find themselves in a position where their troops are being killed every day. This is why they must now leave."
Commenting on comments by Tony Blair, the British prime minister, that Iran and Syria may have a role to play in the future stability of Iraq, he said: "Iran and Syria cannot get involved in Iraq's politics. This will not solve our problems."