U.S. Secretary of Defense Ash Carter is meeting Kurdish leaders during an unannounced visit to the capital of Iraq's Kurdistan Region.
Carter landed early Friday in Irbil, where he is expected to confer with the Kurdistan President Masoud Barzani, a key ally of Washington.
Kurdish peshmerga fighters have emerged as one of the most capable forces in the battle against Islamic State extremists in northern Iraq's autonomous Kurdish region and in neighboring Syria.
The U.S. is providing security assistance to the peshmerga, but Barzani has repeatedly complained this support is not enough to successfully fight Islamic State militants.
Carter arrived in Kurdistan a day after visiting Baghdad, where he took a firsthand look at joint U.S. and Iraqi army efforts to thwart the advances of Islamic State militants.
Iraqi officials strongly criticized the Pentagon chief in May, after he complained Iraqi troops "showed no will to fight" as the insurgents overran Ramadi, the Anbar provincial capital.
But at the first stop of a daylong visit Thursday, Carter praised Iraqi counterterrorism troops, dressed in their trademark all-black uniforms, as he watched their maneuvers at a firing range.
"Your forces have performed so very well, so very bravely," Carter told Iraqi counterterrorism commanders.
"And I know that you have suffered great losses, too, but I just wanted to tell you that it is very clear to us in Washington what a capable force this is. So it is a privilege for us to be your partners," he said.
Pentagon spokesman Colonel Steve Warren, traveling with Carter, told reporters the Iraqi forces, in combination with U.S. airstrikes, are in the "very early stages" of trying to retake Ramadi, now controlled by 1,000 to 2,000 Islamic State fighters.
Warren said Iraqi forces, who are being advised by U.S. troops, are "beginning to isolate Ramadi from multiple avenues of approach" in an attempt to "place a noose around around the city."
"What we're doing is isolating Ramadi," Warren said. "Eventually, when the conditions are right, we will transition into an assault to seize Ramadi."
The United States has nearly 3,400 advisers and trainers in Iraq, but President Barack Obama has balked at calls from some Republican lawmakers to send American ground troops to join Iraqi fighters.
U.S. opinion surveys indicate a majority of Americans are against the reintroduction of U.S. troops in Iraq, which Obama withdrew in late 2011 as the eight-year American war in Iraq ended.
Carter is making his first trip to Iraq as defense secretary. He also visited Israel, Jordan and Saudi Arabia this week.