The remarks by Admiral Mike Mullen, outgoing chairman of the Joint Chiefs of Staff, came ahead of a meeting of Iraqi political leaders to discuss whether to keep any American soldiers in the country beyond a year-end pullout deadline.
Following talks on Monday evening with Prime Minister Nuri al-Maliki and President Jalal Talabani, Mullen said he was confident they were aware of the urgency of the issue, but added that they faced internal political challenges to reach a deal.
"Time is quickly running out for us to be able to consider any other course," Mullen told reporters at a news conference at the US military's Victory Base Camp on the outskirts of the Iraqi capital.
"We really need a decision now. ... I am hopeful that a decision by the Iraqi leadership to enter negotiations with the US is made very quickly."
He insisted, however, that any deal would require parliamentary approval stating that US soldiers stationed in Iraq would enjoy immunity from prosecution.
Under the terms of a bilateral security pact signed in 2008, which calls for all remaining American troops to leave by the end of 2011, US soldiers are immune from prosecution under Iraqi law.
American officials have pressed their Iraqi counterparts to decide quickly whether they want US troops to remain in Iraq beyond December 31, including during a visit in July by Defence Secretary Leon Panetta.
Proposals for a training mission are gaining traction among Iraqi leaders, although nothing has yet been agreed.
Iraqi politicians have already missed a self-imposed July 23 deadline to reach a decision on the US troop presence, and political progress is rarely made during the month of Ramadan, which began on Monday in Iraq.
Maliki said during his meeting with Mullen on Monday evening that he hoped Iraqi political leaders would reach a decision during a meeting -- repeatedly delayed -- now set for Tuesday.
The premier also pressed for continuous cooperation between the two countries regardless of the outcome of the meeting, especially on the subject of air defence, according to a statement from his office.
Iraq has restarted talks with the United States to purchase 36 American F-16 fighter jets, double the figure that had originally been mooted.
Iraq and the US had been close to a final agreement on the F-16s deal earlier this year, but nationwide protests forced the Baghdad government to divert funds earmarked for the warplanes to programmes to help the poor.
US and Iraqi military officials often remark that while they assess Iraq's security forces to be capable of maintaining internal security, the country is lacking in terms of defending its borders, airspace and territorial waters.
Mullen arrived in Iraq on Monday after a two-day trip to Afghanistan, much of which was spent visiting troops before he is due to step down in October.
His Iraq visit comes days after the US Special Inspector General for Iraq Reconstruction, Stuart Bowen, warned in a report that the country was less safe than one year ago and that security was deteriorating.
Figures released on Monday showed the number of Iraqis killed as a result of violence in July declined from the previous month, but still marked the second-highest such toll for 2011.
A total of 259 Iraqis -- 159 civilians, 56 policemen and 44 soldiers -- died in attacks last month.
Copyright AFP (Agence France-Presse), 2011