"We think there is a real likelihood Iran will make a mistake and make a decision to go after some of our forces, military forces in Iraq or soldiers in northeast Syria," he told Fox News in remarks aired Sunday.

His comments came as the military advisor to Iran's supreme leader said there would be a "military" response "against military sites" by Tehran after the killing of Qasem Soleimani, the powerful commander of Iran's Quds Force, the foreign operations arm of its Revolutionary Guards.

"It would be a big mistake for Iran to go after them," Pompeo told Fox.

The US has about 60,000 troops in the region, including around 5,200 in Iraq. Washington ordered thousands more soldiers to the region on Friday after Soleimani's killing.

"We're preparing for all kinds of various responses," including cyber attacks, Pompeo told Fox.