US Defence Secretary Robert Gates has said he favours a "pause" in troop reductions in Iraq after up to 30,000 US soldiers are sent home this summer.
Baghdad was rocked by car bombs as Mr Gates prepared to leave
The Pentagon aims to decrease troop numbers in Iraq from 20 to 15 brigades. One brigade has already left, the last of the five is due to leave by July.
After meeting the US commander in Iraq, Gen David Petraeus, Mr Gates said he wanted a "period of evaluation".
The US deployed an extra 30,000 troops last year to boost security in Iraq.
As Mr Gates acknowledged the situation in Iraq remained "fragile" despite a fall in violence, two explosions rocked Baghdad on Monday.
At least 11 people died in the double car bombing at a petrol station in the city's southern district of Jadriya.
Thirty people were wounded, including the leader of the al-Dulaimi tribe in Ramadi, Sheikh Ali Hatim Suleiman, and the former police chief of the city.
Mr Gates told reporters at a US base in the Iraqi capital on Monday: "A brief period of consolidation and evaluation probably does make sense.
Monday's blasts sent smoke billowing over Baghdad's skyline
"But one of the keys is how long is that period and then what happens after that."
Mr Gates made clear that US President George W Bush would have the final say on troop levels in Iraq.
The defence secretary has previously expressed hope that the drawdown could continue until 10 brigades remained by the end of 2008.
But there have been fears that recent security gains could be reversed if too many troops are withdrawn too soon.
Mr Gates arrived on Sunday for a surprise two-day visit to assess the situation in the country following last year's surge in US force levels.
The deployment of 30,000 extra American troops and the flourishing of Sunni Arab neighbourhood militias that teamed up with the US to fight al-Qaeda in Iraq has been credited with a fall in violence levels in recent months.
Rolling brigade reductions are due to bring the US force back to pre-surge levels of 130,000 by July.
Gen Petraeus is due to make recommendations in the next couple of months on US force levels for the second half of the year.
The BBC's Jim Muir in Baghdad says the situation in Iraq is a lot better than it was six or nine months ago, but is far from perfect, even in Baghdad, which has been the main focus of much of the troop surge.
More than 30 people died in a car bomb in the town of Balad, near Baghdad, on Sunday during the first day of the US defence secretary's visit.