Pompeo was asked on ABC's "This Week" 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."
The laws of armed conflict prohibit the deliberate targeting of cultural sites under most circumstances.
"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 also said the Trump administration has abandoned the previous U.S. administration's focus on countering Iranian proxy groups and suggested the U.S. strike in Baghdad that killed Iranian Gen. Qassem Soleimani was an example of the new strategy.
"We're going to respond against the actual decision-makers, the people who are causing this threat from the Islamic Republic of Iran," Pompeo said.
In Baghdad on Sunday, the U.S. coalition combating the Islamic State group in Iraq and Syria announced that it has "paused" training of Iraqi security forces in order to focus on protecting coalition personnel.