U.S. Defense Secretary Ash Carter arrived in Iraq Saturday to meet with his commanders and assess the progress in the opening days of the operation to retake the northern city of Mosul from Islamic State (ISIS) militants.

His unannounced visit comes two days after a U.S. service member was killed outside Mosul, underscoring the risk that American troops are taking as they advise Iraqi forces in the fight. And it comes on the heels of meetings Carter had with Turkish leaders in Ankara Friday when he announced there "is an agreement in principle" for Turkey to play a role in the battle to retake Mosul, and that friction between Turkey and Iraq can be worked out.

This is Carter's third trip to Iraq this year, and he has overseen the steady increase in the number of U.S. forces deployed to the fight and the growth of America's effort to train and advise Iraqi troops. In his past two stops in Iraq, Carter announced White House decisions to increase the U.S. troop level there. There are no expectations that he will do that again this time.

Instead, he will meet with Iraqi leaders and military commanders to determine how the fight is going and whether or not any changes, increased resources or other assistance is needed.

Carter's meetings in Turkey signal moves to tamp down escalating tensions between Turkey and Iraq over Turkish military operations in northern Iraq. The divide has only grown as the operation to retake Mosul began to take shape.

There are some 500 Turkish troops at a base north of Mosul who have been training Sunni and Kurdish fighters since last December. Baghdad says the troops are there without permission and has called on them to withdraw. Ankara has refused, and insists it will play a role in liberating the city.

The U.S. service member killed earlier this week was the fourth U.S. combat death in Iraq since the U.S. began military operations against ISIS in August 2014. It was the first since the Mosul operation began, and the service member was working with Iraqi special forces northeast of Mosul and serving as an explosive ordnance disposal specialist.

U.S. defense and military officials have said that while the offensive has started well, they expect the complex fight for the city to get more difficult. And they said they will be watching to see how aggressively the ISIS militants fight for Mosul, or if more leaders flee the city.

Meanwhile, in what officials thought was an attempted diversion from the Mosul fight, ISIS attacked targets in and around the northern Iraqi city of Kirkuk on Friday in a coordinated assault that killed at least 14 people.

Carter is expected to meet with Iraqi Prime Minister Haider al-Abadi as well as other top officials.

A U.S. military officer said the Islamic State group has set up a multi-layered defense in and around Mosul. The outer rings of this defense are what the U.S. military calls disruption zones, where ISIS fighters are expected to counter the Iraqi advance through the use of mortars and rockets, suicide bombers, road obstacles and car bombs.

The official said the US does not expect this to include high-intensity force-on-force combat in these outer rings; the expected ISIS focus will be on disrupting and delaying the Iraqi advance rather than trying to hold ground outside the city. The official was not authorized to discuss the matter publicly, so spoke on condition of anonymity.

The U.S. estimates there are between 3,000 and 5,000 ISIS fighters in the Mosul area, but some of the top leaders have likely fled the city. A key factor will be how long those mid-level commanders stay in the city, or if they decide to leave.

The U.S. is uncertain how hard ISIS will defend Mosul. But, once the fighting gets to the center of the city, ISIS will have certain advantages that are more favorable for the use of snipers and the restriction of vehicle movement.

More than 4,800 U.S. troops are in Iraq and there are more than 100 U.S. special operations forces operating with Iraqi units. Hundreds more U.S. forces are playing a support role in staging bases farther from the front lines.