Secretary of State Mike Pompeo said Sunday the U.S. strategy in countering Iran is to target the country's "actual decision-makers” rather than to focus on Iranian proxy forces in Iraq and elsewhere in the Middle East.

Pompeo was explaining U.S. strategy in the aftermath of the U.S. drone strike that killed Iran's most powerful general, Qassem Soleimani, who was mastermind of the country's military operations outside Iran. That killing has sent shock waves across the Middle East, with expectations that Iran will make good on its threat to strike back, with unpredictable consequences for the U.S. and the rest of the world.

Pompeo spoke on ABC's “This Week” amid rising uncertainty about next steps in the U.S.-Iran crisis and the breadth of its ramifications. The U.S. acknowledged an attack Sunday by an al-Qaida affiliate on a Kenyan airfield used by American military forces. It was not immediately clear whether there were U.S. casualties.

In Beirut, Lebanon's Hezbollah chief, Hassan Nasrallah, said the U.S. military in the region, including bases and warships, were fair targets after the killing of Soleimani. Hezbollah is a primary ally of Iran with broad influence. The U.S. has tens of thousands of troops throughout the region, including in Iraq, Syria, Saudi Arabia, Kuwait and Qatar — all within range of Iran or its proxy militias.

Iraq's parliament on Sunday called for the expulsion of U.S. troops from the country in the wake of the attack in Baghdad that killed Soleimani. There are 5,200 American forces in Iraq. At issue is the fate of the agreement under which Washington sent troops to Iraq more than four years ago to help in the fight against the Islamic State group.

Meantime, the U.S. coalition combating IS in Iraq and Syria announced that it has “paused” training of Iraqi security forces in order to focus on protecting coalition personnel.

Pompeo strongly criticized the Iran policy of the Obama administration, saying it fruitlessly focused on Iranían proxies rather than on Iran itself.

He said the U.S. had previously sought to “challenge and attack everybody who was running around with an AK-47 or a piece of indirect artillery. We've made a very different approach. We've told the Iranian regime, 'Enough. You can't get away with using proxy forces and think your homeland will be safe and secure.' We're going to respond against the actual decision-makers, the people who are causing this threat from the Islamic Republic of Iran."

In that context, Pompeo said that if the U.S. military were to strike inside Iran, in the event Iran retaliated against America for the Soleimani killing, those strikes would be legal under the laws of armed conflict.

“We'll behave inside the system,” Pompeo said. “We always have and we always will.”

Pompeo was responding to a question about President Donald Trump's assertion Saturday on Twitter that the United States has 52 Iranian targets in its sights, “some at a very high level & important to Iran & the Iranian culture.”

Targeting cultural sites is a war crime under the 1954 Hague Convention for the protection of cultural sites. The U.N. Security Council also passed unanimously a resolution in 2017 condemning the destruction of heritage sites. Attacks by IS and other armed factions in Syria and Iraq prompted that vote.

“Every target that we strike will be a lawful target, and it will be a target designed with a singular mission — defending and protecting America,” Pompeo said. He did not explicitly contradict Trump on targeting cultural sites. In insisting that any U.S. attacks will be legal, Pompeo said Trump “was getting to this point” without making it in his tweet Saturday.