The US and Iraq have already signed a Status of Forces Agreement, which mandates the presence of US combat troops in Iraq until the end of 2011.
The vote will mostly affect the presence of forces from Britain, which has in place about 4,100 men and women in the south of the country.
Australia, Estonia, Romania and El Salvador also have troops in Iraq.
Confusion over bill
Discussion over the bill mandating the presence of non-US forces has been confused in recent days.
During debates on Saturday, some MPs thought that they were voting against the proposed law on non-US forces but others thought the vote was to invalidate the decision made in an earlier reading.
Gordon Brown, Britain's prime minister, said last week that British troops would end their mission in Iraq by the end of May.
All but 400 solidiers would have left Iraq by the end of July, he said.
Britain's defence secretary said that he expected the Iraqi parliament to have a deal in place by the end the year and said a strategy is in place if no bill is passed.
"We have contingency plans. The safety of our guys out there is our top priority. There will have to be an agreement, a proper agreement, before our guys are out on the streets."
Tony Blair, Brown's predecessor, faced public anger over his decision to be the United States' main partner in the March 2003 invasion that removed Saddam Hussein from power.
At least 178 British soldiers have died in Iraq since the war began, including 136 in hostile incidents.