BAGHDAD – Iraqi leaders must decide “within weeks” whether they want American troops to stay beyond a year-end deadline for their withdrawal, the top U.S. military official said Friday.

“Time is running short,” said Adm. Mike Mullen, chairman of the Joint Chiefs of Staff, who warned that in coming weeks the military must make “irrevocable” logistics and operational decisions about whether to stay or go.

“There is what I call a physics problem,” Mullen said in a visit to Baghdad. “With 47,000 troops here and lots of equipment, physically it just takes time to move them.”

Mullen’s message comes two weeks after Defense Secretary Robert Gates told Iraqi Prime Minister Nouri al-Maliki that some U.S. troops would stay if the Iraqi government requested, an overture that House Speaker John Boehner, R-Ohio, seemed to reinforce during his visit to Baghdad last week.

Under a three-year-old agreement between the two countries, all U.S. troops must leave Iraq by Dec. 31. President Obama, who campaigned on a pledge to get troops out of the country, has not sought an extension of the agreement. But amid mounting turmoil across the Mideast and concern that extremists will try to destabilize Iraq after U.S. forces leave, American military officials have in recent weeks honed a message that if Iraq wants troops to stay, the United States would listen.

Mullen’s short timetable for a response increases pressure on Maliki. Since Gates’ visit, it has become clear that inviting the U.S. military to stay could be politically perilous for the prime minister.

Firebrand Shiite cleric Moqtada al-Sadr warned that he would reconstitute his Mahdi Army militia if the Iraqi government allows U.S. forces to stay.

Other Shiite extremist groups tied to Iran also said they would join against the government and any Americans who remain in the country.

After meeting with Mullen on Thursday, Maliki released a statement on his website saying Iraqi military and security forces have become “able to take the responsibility” for the country’s security.

Still, Iraqis have not viewed Maliki’s statements as unequivocal.