Washington (CNN) Secretary of State Mike Pompeo issued a stark warning to Iran Friday, telling CNN that Washington will take direct action against Tehran for any attacks, even those using proxy forces, against US interests.

JUST WATCHED Pompeo threatens Iran, slams John Kerry Replay More Videos ... MUST WATCH Pompeo threatens Iran, slams John Kerry 06:48

"We have told the Islamic Republic of Iran that using a proxy force to attack an American interest will not prevent us from responding against the prime actor," Pompeo told CNN in an interview with Elise Labott. "We will not let Iran get away with using a proxy force to attack an American interest; Iran will be held accountable for those incidents."

Asked if that meant militarily, Pompeo said, "they're going to be held accountable."

The top US diplomat was speaking in the wake of early September rocket attacks, allegedly by Iran-backed militias, that appeared to target US missions in Iraq, including in an area that houses the US Embassy in Baghdad, the capital of Iraq. The White House blamed Shia militia groups, saying in a Sept. 11 statement that "Iran did not act to stop these attacks by its proxies in Iraq, which it has supported with funding, training and weapons."

Iran's Foreign Ministry responded on September 12 with a statement that called the US claims "astonishing, provocative, and irresponsible."

Read More