According to an official of one of Iraq's most powerful political parties - the Supreme Iraqi Islamic Council (SIIC), US soldiers may have to remain in volatile cities such as Mosul and Baquba.
"There is the pull-out agreement and there is a schedule for that, but scheduling is related to developments on the ground," Mohammed al-Gharawi said.
"No Iraqi, in the government or among the people, wants foreign troops in Iraq. But we work hard to have the security and stability we now have and if the foreign troops need to stay in certain cities to maintain that, why not? Then when all is secure, they can move out."
The remarks come as prominent Iraqi politicians oppose keeping US combat troops in urban areas after the June deadline, and speak of preparedness of Iraqi government forces to restore security and stability and to counter the insurgents.
The new governor of Mosul says that the departure of US troops from the city will actually reduce violence, since much of the violence is directed at the Americans.
"A US withdrawal will reduce the number of targets," Gov. Atheel al-Nujaifi said. "We believe it's important for US troops to stay in camps outside the cities to provide help only if needed."
Nevertheless, recent bomb attacks together with the murder of a leading Sunni figure, Harith al-Obaidi, have stoked public fears of resurgence of sectarian bloodshed.
US officials believe that security in Iraq remains fragile since the various religious and ethnic groups have still not reached consensus on power-sharing arrangements necessary for long-term stability.