Trump was accused of threatening a war crime after he tweeted that sites which were "important to Iranian culture" were on a list of 52 potential US targets should the regime in Tehran make good on its pledge to avenge the killing of a top commander.

Asked in a television interview why Trump was threatening Iran with a war crime, Pompeo said: "We'll behave lawfully. We'll behave inside the system.

"We always have and we always will," Pompeo told the ABC network's "This Week" program.

Pompeo refused to give any details on the potential targets but said Trump would "never shy away from protecting America.

"I've seen what we are planning in terms of the target set. I'm sure the Department of Defense is continuing to develop options," he said.

"The American people should know that every target that we strike will be a lawful target, and it will be a target designed with a singular mission, of protecting and defending America."

Trump's threat late Saturday sparked widespread accusations from Democrats that he would be in breach of the Geneva Convention which says any targeting of cultural sites constitutes a war crime.

"You are threatening to commit war crimes. We are not at war with Iran. The American people do not want a war with Iran," Senator Elizabeth Warren, one of the top Democrats hoping to challenge Trump in November's election, wrote on Twitter.

Iran's Foreign Minister Mohammad Javad Zarif also tweeted that "targeting cultural sites is a WAR CRIME".