BAGHDAD >> The combat death today of a U.S Navy SEAL who was advising Kurdish forces in Iraq coincides with a gradually deepening American role in fighting a resilient Islamic State, even as the Iraqis struggle to muster the military and political strength to defeat the militants.

The SEAL, who has not been further identified, is the third American serviceman to die in combat in Iraq since the U.S.-led coalition launched its campaign against the Islamic State in the summer of 2014. Seven months ago, a special operations soldier, 39-year-old Master Sgt. Joshua L. Wheeler, was killed during a Kurdish-led raid on an Islamic State prison in northern Iraq. In March, a Marine artilleryman, Staff Sgt. Louis F. Cardin, 27, was killed when the militants launched a rocket attack on a newly established U.S. firebase outside Mosul.

Over the course of the campaign, the Pentagon has slowly expanded the American military role. The strategy, criticized by some as incremental and inadequate, aims to ensure that the Iraqis do the ground combat, supported by U.S. airpower, special operations advisers and others. As the Iraqis have gained competence and confidence and prepared an assault in hopes of retaking Mosul, the Pentagon has announced plans to put more U.S. troops in Iraq and place them closer to the front lines.

In Defense Secretary Ash Carter’s view, that means a greater chance for success. It also means more risk to U.S. troops, as he acknowledged Tuesday in announcing the latest death.

“It shows you it’s a serious fight that we have to wage in Iraq,” Carter said.

White House spokesman Josh Earnest said President Barack Obama had been briefed on the incident and extended condolences to the family of the service member killed in northern Iraq. Earnest said the incident was a “vivid reminder” of the dangers facing U.S. troops in Iraq and Syria.

“They are taking grave risks to protect our country. We owe them a deep debt of gratitude,” Earnest said.

Tuesday’s U.S. death coincides with diverging trends in Iraq. On one hand, Iraqi forces trained and advised by Americans have scored significant battlefield gains in recent months, including the recapture of Ramadi and other advances against IS-held towns in Anbar province. On the other hand, political conflict in Baghdad fed by sectarian rivalry is threatening to derail the entire effort.

Carter said on Monday that as the Iraqis gain battlefield momentum the Pentagon will pursue additional ways to support them,. Recently that has meant adding more U.S. troops to advise Iraqi brigade and battalion commanders closer to the fight. Inevitably that means the likelihood of more U.S. combat casualties, even though the White House insists there are no U.S. “boots on the ground” in Iraq or Syria.

The risk can be expected to grow if, as planned, the U.S. sends Apache attack helicopters into battle in support of an Iraqi assault on Mosul in coming months. The U.S. also has committed to sending more mobile artillery as part of that effort and to providing up to $415 million in support of the Kurds in northern Iraq. Obama recently authorized an increase in the number of troops that can deploy to Iraq to advise and assist Iraqi forces. The cap was increased last week from 3,870 to 4,087.

The U.S. also has announced it will increase the number of special operations forces in Syria from 50 to 300.

As described by an Iraqi Kurdish intelligence officer, Lt. Col. Manav Dosky, Tuesday’s Islamic State attack was launched on Teleskof, about 14 miles north of Mosul, just after 6 a.m. The Islamic State broke through the Kurds’ front-line position with a barrage of armored Humvees and bulldozers, Dosky said, and clashes killed at least three Kurdish peshmerga fighters. The SEAL was among Americans advising the peshmerga during that battle.

Maj. Gen. Jaber Yawer, a Kurdish peshmerga spokesman, told The Associated Press that the American was killed by IS sniper fire during an IS attack that also involved a number of car bombs.

A U.S. defense official, speaking on condition of anonymity because he wasn’t authorized to discuss the incident publicly, said the American was killed with small arms fire, suggesting that Islamic State fighters likely came within a few hundred yards of the U.S. forces.

The Americans were two to three miles behind that front line before the attack was launched, the official added.

American forces will continue to stay behind the front lines, the defense official said, but he acknowledged that the U.S. expects more ground fighting as the Iraqi and Kurdish militaries, backed by the U.S., push farther into Islamic State-controlled territory.