Senior US general Richard Myers says civilians who fled the fighting in the Iraqi city of Falluja last month will soon be able to return home.
Unexploded ordnance is one of the current dangers in Falluja
On a visit to Iraq, the chairman of the Joint Chiefs of Staff said there were still pockets of resistance in the city and citizens would return gradually.
He also said high levels of US troops would remain in Iraq ahead of nationwide elections on 30 January.
In Baghdad, a checkpoint was hit by its second car bomb attack in two days.
At least 12 people were wounded in the blast outside the government and diplomatic compound known as the Green Zone. On Monday, seven people were killed in a similar attack.
Gen Myers told a press conference in Baghdad that he expected some of the 200,000 citizens who fled Falluja to start returning in the next few days.
"They are going to sequence that, going by certain sections of the city, it won't be the whole city at one time," he said.
He said "unexploded ordnance" was one of the problems inhibiting civilians' return.
There have been American air strikes and renewed clashes between US troops and insurgents in Falluja in the last few days.
"What we are seeing now are some remnants of fighters and insurgents in Falluja that are being dealt with, although we have reports of a few insurgents trying to filter back in with ordinary Falluja citizens," he said.
A US marine in the city, Capt Paul Batty, said his troops were now fighting mostly foreign rebels prepared to die for their cause.
"Right now we are fighting fanatics - it's way beyond the money question. You would need millions of dollars to get an ordinary person to live this life," he was quoted by the AFP news agency as saying.
Gen Myers told reporters the US would only reverse its troop levels when "events on the ground" allowed.
"Our troop levels will be at 150,000 during the election and a little bit after," he was quoted by the Associated Press as saying.