BAGHDAD (AP) — Even with the burdens of combat in Afghanistan and unrest in the Arab world, the U.S. would keep American troops in Iraq beyond the agreed 2011 final withdrawal date if Iraq’s government asked for extra help, Defense Secretary Robert Gates said Thursday.

His comments give weight to an idea that is politically sensitive in both nations and which Iraq officially rejects.

During what he said would probably be his final visit to Iraq as Pentagon chief, Gates urged the fractious Iraqi government to decide “pretty quickly” whether it wants to extend the U.S. presence beyond Dec. 31 to enable continued training of its security forces. Gates shares the view of many in the U.S. military that a longer U.S. stay would be useful in ensuring that Iraq’s security and political gains do not unravel, but publicly he has insisted that the decision is Iraq’s.

“We are willing to have a presence beyond (2011), but we’ve got a lot of commitments,” Gates said during a question-and-answer session with troops at a U.S. military compound on the outskirts of Baghdad. He cited U.S. military involvement in Afghanistan and Libya and noted that few people realize that 19 U.S. Navy ships and about 18,000 U.S. military personnel are assisting in earthquake, tsunami and nuclear reactor relief efforts in Japan.

“So if folks here are going to want us to have a presence, we’re going to need to get on with it pretty quickly in terms of our planning,” he added. “I think there is interest in having a continuing presence. The politics are such that we’ll just have to wait and see because the initiative ultimately has to come from the Iraqis.”

The American military presence is broadly unpopular in Iraq, even though many Iraqis say they are glad that the U.S.-led war toppled dictator Saddam Hussein. Many Iraqis say the visible presence of U.S. forces is a slight to their national pride, and unnecessary eight years after the start of the war.

Iraq’s perpetually squabbling politicians are wary of suggesting that the country cannot stand on its own, for fear that rivals could exploit such a statement.

Gates’ press secretary, Geoff Morrell said it was clear from Thursday’s talks that al-Maliki does want US troops to stay beyond 2011.

“It is our sense that there is a recognition on the part of Iraqi leaders that there is still a need for US forces in some capacity,” Morrell said.

The main problem is selling an extension to a skeptical Iraqi public. There are persistent rumors on the street that the U.S. has ulterior motives in Iraq, and wants to stay to keep a better foothold in the Middle East instead of as a backstop to Iraq’s national defenses.

U.S. officials reject that outright, saying they have no desire or plan for a permanent military footprint in the country.

Prime Minister Nouri al-Maliki told Gates that he expects all U.S. troops to be out of Iraq by the end of the year as required under a 2008 security agreement between Baghdad and Washington, said Iraqi government spokesman Ali al-Dabbagh.

“The prime minister informed Gates that the Iraqi government does not want the presence of the American forces in their current position,” al-Dabbagh told The AP after al-Maliki’s meeting with Gates. “We think that the presence of these forces is not suitable for Iraq, and these forces have to leave by the end of 2011.”

A government statement said Iraq’s security forces are up to the task “to repel any aggression.”

The prime minister stressed that Iraqi security forces, both the police and army, now have the capabilities to repel any aggression, and that the capabilities of our security forces to impose security and stability are constantly improving, according to the statement.

However, al-Maliki, who barely held onto his job last year after his party failed to win the most parliamentary seats in national elections, maintained that a small number of American troops might stay past 2011 as part of a training office within the U.S. Embassy in Baghdad.

Al-Maliki is under pressure from the political wing of hardcore Shiite followers of anti-American cleric Muqtada al-Sadr who are threatening to revolt if American troops stay past the end of the year — despite the fragile security in Iraq, where people continue to die nearly every day in bombings and shootings.

Last week, U.S. Ambassador to Iraq James F. Jeffrey estimated there would be no more than 200 U.S. forces and civilian Defense Department employees in that office.

“After the departure of the current forces and the purchasing of weapons, there must be some forces present here for training,” al-Dabbagh said Thursday. “But the presence of the forces in their current position won’t be extended.”

In separate remarks Thursday, the top American commander in Iraq, said that country is lacking in important security capabilities, including the defense of its air space and the wherewithal to supply and maintain its own forces.

Asked whether all Iraqi government officials are aware of these gaps, Army Gen. Lloyd Austin replied, “Some more than others.”

Speaking to a group of reporters traveling with Gates, Austin gave the strong impression that he thinks Iraq needs a U.S. military presence beyond December, but he said he had not yet been asked to provide a recommendation to Washington. He said Iraq faced the possibility of a “more violent environment” next year, in the absence of U.S. troops, if it cannot resolve political problems like the Kurd-Arab tensions in Kirkuk and elsewhere in the north.

Austin said that because of the relentless insurgency that consumed Iraq until recently, the U.S. military has not focused “in earnest” on training and equipping Iraqi security forces to defend against outside threats. He noted, for example, that Iraq’s army will be receiving modern tanks and artillery just at the scheduled end of U.S. military involvement in December. It has little in the way of an air force, and its intelligence agencies are weak.

Austin said Prime Minister Nouri al-Maliki’s failure thus far to appoint a defense minister and an interior miniter — the two officials most directly responsible for security forces — has complicated their process of deciding whether to invite the Obama administration to negotiate a new legal document to permit U.S. forces to remain here beyond December.

“The clock is ticking,” Austin said.

The U.S. now has about 47,000 troops in Iraq, and they will begin leaving in large numbers in late summer or early fall. The U.S. led an invasion in March 2003 that toppled the government of President Saddam Hussein a month later, but an insurgency soon set in and the U.S. got mired in a conflict that has lasted far longer — and cost far more American and Iraqi lives — than Washington had anticipated.

In a brief exchange with reporters during a photo session with Gates earlier Thursday, the U.S. ambassador to Baghdad, James Jeffrey, said U.S. ground forces are “the glue” that is holding the country together. He said this leaves a mixed picture of the situation in Iraq because making arrangements to keep U.S. troops here beyond December is going to be difficult.

Among Americans, attention to Iraq’s future has waned as violence here dropped off and the U.S. withdrawal date approaches.

Meghan O’Sullivan, a top Iraq adviser to President George W. Bush from 2005-07, said in an email exchange that al-Maliki faces enormous domestic political pressures on several fronts, including a small but vocal number of Iraqis demanding better government, and a security situation that is improved but still tense.

Together, these pressures make it difficult for al-Maliki to feel he can publicly invite the U.S. military to stay beyond this year.

“Understandably, the Obama administration was hoping for this sort of invitation, and likely feels struck, given that it is not forthcoming,” said O’Sullivan, now a professor of international affairs at Harvard University’s John F. Kennedy School. “They can’t be seen wanting to keep more troops in Iraq than the Iraqis do.”

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Associated Press writers Qassim Abdul-Zahra and Lara Jakes in Baghdad contributed to this report.