The US government does not want an "arbitrary date" for troop withdrawal
The US and Iraq are unlikely to come to an agreement on a long-term security pact before the 31 July deadline, White House spokeswoman Dana Perino has said.
"I don't think that we'll be able to finalise this agreement by next Thursday... it might take a few more days after that," said Ms Perino.
The two countries are hammering out a deal to allow US troops to stay in Iraq after the current UN mandate runs out.
The UN resolution authorising the US presence expires on 31 December 2008.
The 31 July deadline is a self-imposed time-limit, so missing it would not have any impact on the legality of the US military's presence in Iraq.
But correspondents say the delay suggests that there are serious disagreements between the US and Iraq over the future of American forces in the country.
One of the sticking points in the negotiations has been the inclusion in the deal of a timetable for the withdrawal of US troops from Iraq.
The Iraqi government has indicated that it would be in favour of including such a timetable, while the US government is committed to removing troops only when it determines that conditions on the ground allow it.
Last week, the two governments agreed to include a "general time horizon" for troop withdrawal in the deal, although the US stressed that no "arbitrary date" for the removal of troops would be included in the agreement.
But Ms Perino has indicated that the pact might contain an "aspirational date" for the end of the US presence in Iraq.
"It might be something along the lines of 'we think that Iraq would be able to take over its security for all of its provinces by this aspirational date'," she told reporters.
"But I don't know exactly how it's going to read... it would not include anything about troop levels."
A timetable for troop withdrawal has been a point of contention in the US presidential election campaign.
Democratic contender Barack Obama has pledged to remove US combat troops from Iraq within 16 months of coming to office, while his Republican rival John McCain has committed himself to removing troops only if conditions are favourable.
On Saturday, Iraqi Prime Minister Nouri al-Maliki was quoted in the German magazine Der Spiegel, apparently giving his support to Mr Obama's 16-month withdrawal proposal.
"US presidential candidate Barack Obama is right when he talks about 16 months," the magazine quoted him as saying.
An Iraqi government spokesman later said that Mr Maliki's words had been mistranslated, although the magazine has maintained that its story was correct.