Air Force commandos are already operating in the war against the Islamic State, the head of Air Force Special Operations Command said Monday.

"When you have a campaign against violent extremist organizations, which this is – this is one violent, extremist organization – and when you think of the nature of that conflict over there and you think about special operations forces, you've got to think we have a piece of the action," Air Force Lt. Gen. Bradley Heithold said at the Air Force Association's Air & Space Conference.

Heithold would not reveal types and numbers of aircraft and personnel involved. He also would not confirm the nature of their missions, but he said AFSOC airmen had arrived with the first wave of troops to Iraq.

"Suffice it to say Air Force Special Operations Command is involved," he said. "The capabilities that I bring to the fight are applicable to this particular effort against ISIL."

Heithold's comments came one day before Joint Chiefs of Staff Chairman Gen. Martin Dempsey told the Senate Armed Services Committee that if the current strategy of airstrikes in support of Iraqi and Kurdish forces fails, he would want to put American combat troops on the ground.

"If we reach a point where I think our advisers should accompany any Iraq troops, I'll recommend that to the President," Dempsey said.

President Obama has so far ruled out putting U.S. combat troops into the fight against the Islamic State. For now, air support and leading a coalition of Arab and European nations to destroy ISIL is the White House's stated strategy.

While some European partners have indicated an interest to contributing to the air assaults on ISIL forces, none of the coalition members – except Iraq – have said they would deploy their own soldiers into the war against ISIL.

Dempsey said that while the U.S. continues its current support of Iraq "we will simultaneously pressure ISIL in Syria.

"We will begin building a force of vetted, trained moderate Syrians to take on ISIL," he said. "We will work to ensure that they have a Syrian chain-of-command and report to a moderate political authority."

The U.S. has said it will not ally itself with or coordinate with forces loyal to Syrian President Basher al Assad, who has been waging a war against a number of rebel forces for three years.

-- Bryant Jordan can be reached at bryant.jordan@monster.com