Asked about a potential parliamentary request that U.S. forces depart Iraq, Pompeo said the administration would "have to take a look at what we do when the Iraqi leadership in government makes a decision."

But he added that "the American people should know we'll make the right decision," and will "take actions that frankly the previous administration refused to take to do just that."

Soon after Pompeo's appearance on Fox, the Iraqi parliament formally voted to expel American service members from the country, according to The Associated Press — approving a resolution aimed at forcing the U.S. to withdraw roughly 5,000 soldiers stationed across Iraq.

The State Department later issued a statement regretting the vote.

"The United States is disappointed by the action taken today in the Iraqi Council of Representatives," spokeswoman Morgan Ortagus said. "While we await further clarification on the legal nature and impact of today's resolution, we strongly urge Iraqi leaders to reconsider the importance of the ongoing economic and security relationship between the two countries and the continued presence of the Global Coalition to Defeat ISIS. We believe it is in the shared interests of the United States and Iraq to continue fighting ISIS together. This administration remains committed to a sovereign, stable, and prosperous Iraq."

Experts said that the measure was nonbinding, but that it was hugely consequential given the Iraqi prime minister's own call for U.S. and other foreign forces to leave. Still, there is no clear timetable as to when an exit would unfold, and other regional players — such as the Sunnis and the Kurds — might try to make the case for American troops to stay.

Another wild card is Trump himself, said Rob Malley, president of the International Crisis Group. The president has long said he would prefer to have fewer U.S. entanglements in the Middle East, and if he senses the Iraqis are "ungrateful," he might just opt for a quick withdrawal, Malley said.