Secretary of Defense Ash Carter vowed the U.S. military would conduct more raids against the self-proclaimed Islamic State, even after a recently publicized raid led to the first U.S. combat death since the 2011 withdrawal.

But at the same time, he struggled to call the U.S. effort something other than a combat one, insisting it remained a “train, advise and assist” mission. At one point, however, while describing the circumstances of Master Sgt. Joshua Wheeler’s death during an Iraqi raid earlier this week said: “This is combat, and things are complicated.”

During a press briefing with reporters, Carter also called such raids effective.

“We have this capability. It is a great American strength. It doesn’t represent assuming a combat role,” Carter said, adding: “When we find things that will effectively prosecute the campaign, we are going to do them.”

The Obama administration, which has heralded its 2011 withdrawal from Iraq and its wind down of the U.S. war in Afghanistan, has resisted acknowledging that it has sent troops back to war in Iraq. Indeed, Obama vowed just last year that the U.S. would no longer lose forces in Iraq.

As long as U.S. forces are not engaged in traditional combat fighting of claiming or holding territory, the troops are back, but not in combat, Pentagon officials have suggested. Instead, they are advisers.

But Wheeler’s death, the first since the administration withdrew U.S. troops from Iraq at the end of 2011, made the claim that there was a distinction between advising and combat less convincing.

Carter conceded that troops “will be in harm’s way” in Iraq.

Wheeler—who was on his 15^th tour and had earned a remarkable 11 Bronze Stars—died when Delta forces, alongside their Kurdish counterparts, moved on an ISIS prison holding 70 captives, including 22 Iraqi security forces.

Carter said early reports suggested that U.S. and Kurdish forces were confronted with a firefight upon arrival at the site in the predawn hours, which caught the Kurdish fighters they were advising by surprise. He said Wheeler died when he “ran to the sounds of the gun” to put himself in between Kurdish forces he was advising and jihadists. What is unclear is how close U.S. forces were to the Kurdish troops they were advising.

The Secretary of Defense said he signed off on the raid, in part, because the threat of mass executions was imminent, saying that ISIS had dug graves next to the prison in preparation for death. Pentagon officials said Carter did not know who exactly was being rescued when he approved the raid.

Kurdish officials said the hastily executed raid happened because they feared Kurdish prisoners were about to be killed, but the prisoners turned out to be non-Kurdish.

Wheeler, 39, of Roland, Okla., was reportedly shot in the head and transported to a U.S. base in the northern Iraqi city of Irbil, where he died. His body returns to the United States Saturday, arriving at Dover Air Force Base.

—Nancy A. Youssef