WASHINGTON—Defense Secretary Ash Carter signaled a new and more muscular policy in Iraq and Syria, saying the U.S. military would mount more raids and provide more active support to groups, including Kurdish fighters, who can counter Islamic State.

A day after a dramatic, joint rescue with Kurdish forces near Kirkuk resulted in the first American combat death in Iraq since 2011, Mr. Carter on Friday said there would be more such operations. He also said Americans should gird for a dangerous, complicated fight, but expressed confidence the U.S. would ultimately win.

President Barack Obama has been publicly cautious in his policy against Islamic State, repeatedly saying that American troops wouldn’t participate in combat missions as they battle the extremists across Iraq and Syria.

But while Mr. Carter expressed sorrow for the loss of Master Sgt. Joshua Wheeler in Thursday’s raid, he indicated the beginning of a deeper, more assertive role for American forces there.

“There will be more raids,” Mr. Carter said at the Pentagon. American forces, he said, “will be in harm’s way, there’s no question about it, and I don’t want anybody to be under any illusions about that.”