The Iraqi government isn't likely to ask American troops to remain in the country beyond a 2011 withdrawal deadline, the top U.S. commander in Iraq said Tuesday, despite ongoing violence in some hotspot regions.

Officials also are considering sending several thousand more U.S. soldiers home this year — in addition to 12,000 troops who will leave Iraq by September — if security improves over the next six months, Gen. Ray Odierno told The Associated Press.

Bombings, shootings and other attacks have prompted widespread speculation that Baghdad may re-negotiate its Jan. 1 security agreement to keep U.S. troops in Iraq beyond the deadline.

Under the agreement, all U.S. soldiers are scheduled to leave Iraq at the end of 2011, and President Barack Obama has ordered an end of combat operations by September 2010.

"I think that the Iraq leadership is focused on that this ends in 2011," Odierno said in a half-hour interview.

The general said he has not discussed the possibility of extending the U.S. military's stay — to fight insurgents and train national security forces — with Iraq officials. And it may be too early to predict whether that will happen, Odierno said.

Still, "the progress we're making now and what I see today, I say that I don't see anything that would have us have to re-negotiate in 2011," Odierno said.

"But again, I never say never," he added.

Safety remains unpredictable at best — and has the potential to crater — in north Iraq regions around Mosul, Diyala and Kirkuk, Odierno said. About 60 people have been killed in suicide bombings in the Baghdad area since Sunday.

He cited gains in the areas such as Anbar province, Basra and around Baghdad, where a suicide bomber on Tuesday attacked a market on the edge of the city, killing 33.

If safety improves across Iraq, Odierno said he may send another brigade of soldiers home this fall. That decision will be made in September, he said, after the already-announced departure of 12,000 U.S. soldiers and 4,000 British troops.

The decision will largely hinge on the status of security in Mosul, Diyala and Kirkuk, Odierno said, adding that he wants to see what happens when U.S. combat troops leave cities on June 30.

A brigade consists of about 3,500 troops.

"I could potentially pull out another brigade, and it'll be based on how I see how things have gone," Odierno said.