WASHINGTON (CNN) -- As the deadline nears for U.S. troops to exit major Iraqi cities, units in Mosul are in the midst of a months-long operation to sweep out extremist fighters.
U.S. troops have a deadline of June 30 to exit major Iraqi cities.
The decision on whether to keep troops in the restive northern city beyond June 30 has been a sticking point between the United States and Iraq. Parts of the city remain under insurgent control and high-profile attacks continue, unlike the vast majority of the country.
"We still have a major operation going inside of Mosul with all forces assisting and helping out. We expect that to end here within about 30 to 45 days, and then there will be a decision to be made," the top U.S. commander in Iraq, Gen. Raymond Odierno, told reporters at the Pentagon on Friday.
"I was just up there Saturday, and we conducted a joint assessment," he said. "There's some problems that we have to work through but, in fact, there's potential that they [Iraqi forces] can handle the mission" when they take over in July.
Despite concerns about the continuing violence, the government of Iraq said last week it will not extend the deadline for U.S. combat troops to leave Iraqi cities.
The joint operation to clear Mosul of insurgents has been going on for 75 days, neighborhood by neighborhood, according to Odierno.
"It's going to take us another 30 days to finish that," he said.
Mosul has become the last major fighting ground in Iraq as insurgents, mainly al Qaeda, were pushed north out of Baghdad during the U.S. troop "surge" that started in 2007. Insurgents were able to entrench in the city as U.S. and Iraqi forces cleared and held Baghdad and other regions.
A number of U.S. troops were moved out of Mosul to help with surge operations farther south, leaving Mosul and surrounding areas mainly to Iraqi forces and a smaller U.S. military contingent.
While Odierno said the current operations are "having a good impact," in Mosul, continued high-profile attacks haunt commanders there.
On May 1 a suicide bomb was detonated near a coffee shop, killing at least six people.
Five U.S. soldiers were killed on April 10 when a suicide bomber breached the outer security barrier of Iraqi National Police headquarters in southern Mosul. It was the single deadliest attack on U.S. troops in more than a year, the U.S. military said.
Odierno noted the tactic of using women as suicide bombers is being used by insurgents in Mosul.
"We've seen a few in Mosul -- a couple of attacks were connected by Tunisian foreign fighters that came in, we think, through Syria. We actually detained the leader of the cell, so now we're learning more and more about it," he said.
U.S. and Iraqi forces are also facing a recent increase of attacks in Baghdad, which Odierno and other U.S. military officials pin on al Qaeda trying to again foment sectarian violence.
"We're trying to get inside of these cells. We're trying to understand where they're coming from and we have been successful. We are picking people up," the general said.
He said the United States has improved its intelligence sharing with the Iraqi forces over the past six months, helping to impair the ability of the insurgents to move around.
"Their [Iraqi forces'] strength is the human intelligence. Our strength comes in other ways. And so we're trying to combine those together so we can work toward solving this problem," he said.
But with 45 days left until the security agreement with Iraq takes U.S. troops in Baghdad off the streets and back to their bases, there is some uncertainty about how Iraqi forces will contain the current violence.
Odierno remains positive.
"There's a potential that this could actually work, if the Iraqis are able to maintain in the cities and we're able to, then, to spend more of our time in the support zones outside of the cities," he said.
"We actually could come up with, actually, a stronger method of going after these forces. But we'll have to wait and see."