US military presence could be open-ended under future deal between Bush and Maliki.
Illustrating that point, roadside bombs in Iraq’s capital left four US soldiers dead over the last two days.
The latest attacks bring to 10 the number of Americans who have been killed in Iraq in the past week.
And US forces have been accused of killing Iraqi civilians in three separate attacks over the last two weeks.
Witnesses said American soldiers entered homes overnight and killed whole families, including children, while the US military said troops were forced to respond against “terrorists”.
The two countries are negotiating a new security deal after a United Nations mandate expires on December 31, along with a separate long-term agreement on political, economic and other security ties.
US and Iraqi officials say they hope to finalise the deal by late June or July
The State of Forces Agreement (Sofa) has led to protests in Iraq after media reports said the US was demanding immunity for military contractors and that the deal provided for the presence of up to 50 permanent military bases in the nation – reports later denied by US officials.
However, speaking exclusively to Al Jazeera earlier this month, Hoshyar Zebari, the Iraqi foreign minister, said the US had accepted Iraq’s demand that any new security deal would not include immunity for US contractors working in the country and said the clause would be stated explicitly in the agreement.
“There would be no immunity whatsoever for private contractors because of what we’ve gone through with them in the past and because of the sensitivities for the Iraqi people,” he said.
Zebari said the new agreement would also state that Iraq cannot be used for “any offensive actions” against “any” of Iraq’s neighbouring countries, in reference to ongoing US tensions with Iran over its nuclear programme.
However, the US would be granted control of Iraqi airspace below 10,000m, he said.
The presence of tens of thousands of foreign private security contractors in Iraq has been heavily criticised, especially after the killing last year of 17 Iraqis in Baghdad by Blackwater, a US company which protects US officials in the country.
Zebari also told Al Jazeera the US was showing “great flexibility” and that he was confident the deal would be finalised by the end of June.