George Bush met the Iraq Study Group on Monday and promised to work with the incoming Democratic majority towards "common objectives".
But when asked about proposals by Carl Levin, the Democrat in line to lead the Senate Armed Services Committee, for a phased troop reduction, Bush said: "I believe it is very important ... for people making suggestions to recognise that the best military options depend on the conditions on the ground."
Levin and other Democrats have called for some troops to come home immediately, suggesting that would pressure the Iraqi government into assuming more responsibility.
Levin said the US administration did not see that "we're getting deeper and deeper into a hole".
While most Democrats agree that troops should leave Iraq sooner rather than later, they remain divided on the specifics.
John Murtha, a Pennsylvania Democrat and a contender to become the next majority leader, supports an immediate withdrawal of all troops, arguing that violence in Iraq will continue as long as US troops are present.
Levin and others favour a slower phased withdrawal and have been reluctant to suggest a firm timetable.
The Iraq Study Group, headed by James Baker, the former secretary of state, and Lee Hamilton, a former Democratic representative, has been briefed on the Democrats' proposals and is considering a range of options.
Bush, Dick Cheney, the vice-president, Josh Bolton, the chief of staff and Stephen Hadley, the national security adviser, met the 10-member panel for an hour.
Baker and Hamilton said in a joint statement after the meeting: "We were pleased to meet with senior administration officials today and look forward to our consultations with some top Democrats tomorrow. We are working expeditiously to complete our report and recommendations."
Bush discussed the meeting with reporters during a picture-taking session in the Oval Office with Ehud Olmert, the Israeli president.
He said: "I was impressed by the questions they asked. They want us to succeed in Iraq, just like I want us to succeed. So we had a really good discussion."