Iraq regards blanket immunity for US troops as undermining its sovereignty
Senior Iraqi politicians have adjourned talks on a draft deal with the US that could see the withdrawal of American troops in three years' time.
The agreement has been the subject of negotiations for months, and its approval by the Political Council for National Security is not guaranteed.
There is no indication of when the council will resume its debate.
In Washington, US defence chief Robert Gates is said to be briefing key members of Congress on the deal.
The UN mandate for US-led coalition forces expires at the end of this year.
About 144,000 of the 152,000 foreign troops deployed there are US military personnel.
Although Mr Gates is seeking support from members of Congress on the draft security agreement- details of which have not been released - their approval is not needed.
However, the deal does need approval on the Iraqi side, which correspondents say may be difficult.
Some Iraqi politicians have already criticised the proposed pact.
A Sadrist member of parliament, Nosair Al-Issawi, told the BBC Arabic Service that his bloc wants the US soldiers to leave immediately.
"As a matter of principle we totally reject this agreement because the presence of foreign troops on Iraq's territories is a violation of its sovereignty," he said.
"Neither Iraq nor the Iraqi people can be sovereign in the presence of foreign troops with certain powers [over the country] whatever these powers are."
Iraqi Foreign Minister Hoshyar Zebari has urged politicians to support the deal, saying it will help to protect Iraqi sovereignty.
If there is no final agreement by the end of the year, both sides will have to go back to the United Nations to renew the mandate allowing the presence of US troops in Iraq.
US officials say the deal would see combat forces withdrawn from Iraqi towns and cities by the middle of 2009, and could see US troops withdraw completely by the end of 2011.
However, a Pentagon spokesman said the complete withdrawal "will only be followed if the conditions on the ground provide for it".
The Bush administration has long opposed the idea of a timeline for the withdrawal of US troops.
Mr Gates, Secretary of State Condoleezza Rice and President George W Bush's national security adviser, Stephen Hadley, are said to be reaching out to key members of the House of Representatives and the Senate.
Ms Rice is also said to be pressing senior Iraqi leaders to accept the deal.
Friday's meeting of the Political Council for National Security was the first test for the agreement.
If it eventually wins the council's approval - and that is not expected to be automatic or trouble-free, says the BBC's Jim Muir in Baghdad - that would imply that endorsement by parliament, and the cabinet should follow on relatively smoothly.
Senior Iraqi officials involved in the negotiations say they believe all the outstanding issues have been settled.
President Jalal Talabani (r) has been involved in the talks
The Iraqi government believed that the current immunity from prosecution granted to US troops and contractors by the former Coalition Provisional Authority (CPA) undermined Iraqi sovereignty.
The new draft is said to grant Iraqi judicial authorities limited ability to try US troops and contractors for major crimes committed off-duty or off-base - if a joint US-Iraqi committee agrees.
It is a move that worries some members of the US Congress.
"I am sceptical of any agreement that would subject US servicemen and women to the jurisdiction of Iraqi courts in the middle of a chaotic war," Senator Carl Levin, chairman of the Senate Armed Services Committee, told the Associated Press.
However, a US spokesman said Mr Gates believed it offered adequate protection for US forces in Iraq.
Another difficulty that remains is that any agreement for the continuing presence of US troops in Iraq is anathema to some of the political groups in Iraq, our correspondent says.
The faction loyal to the militant Shia cleric, Moqtada Sadr, is bitterly opposed and a big protest demonstration has been called for Saturday.