By Justin Webb
BBC correspondent in Washington
The Bush administration has received a warning from two senior senators that Iraq faces the possibility of civil war.
Richard Lugar and Joe Biden, the Republic and Democratic Party leaders of the Senate Foreign Relations Committee, said the US should consider postponing the handing over of sovereignty which at the moment is set for 30 June.
Lugar and Biden say a 30 June deadline should be debated
The date is an important political deadline for the White House, which wants to be able to show the American people that it is making progress towards handing Iraqi affairs back to the Iraqi people.
The political fallout from the violence of the last few days in Iraq is beginning to take on worrying proportions for the Bush administration.
Democrat Senator Joe Biden talked over the weekend of the real prospect of civil war in Iraq if the White House sticks to the 30 June deadline for handing over sovereignty.
Mr Biden said Nato should be involved and the UN should be invited to send a commissioner to help run the country.
Mr Biden's Republican colleague, Richard Lugar, also talked of the possibility of civil war.
He said it was time to begin a debate on whether the 30 June handover could still take place.
The Foreign Relations Committee will begin hearings on the subject soon.
The White House is heavily committed to its deadline.
Letting that date slip would send a message to the American people, only months before the presidential election, that Iraq was out of control.