Iran-allied Houthi rebels in neighboring Yemen claimed credit for the attack, saying they sent 10 drones to strike at important facilities in Saudi Arabia’s oil-rich Eastern Province. But Mr. Pompeo said there was no evidence the strikes had come from Yemen.

In a tweet, he said the U.S. will work with allies “to ensure that energy markets remain well supplied and Iran is held accountable for its aggression.” He added that the strikes showed Iran wasn’t serious about diplomacy.

Mr. Pompeo didn’t explain how the U.S. believes Iran was to blame or where the strikes originated, but Iran-backed militias in Iraq have previously been responsible for targeting Saudi Arabia’s oil industry. Meanwhile, Saudi and American officials are investigating the possibility that attacks on Saudi oil facilities Saturday involved cruise missiles launched from Iraq or Iran.

The production shutdown amounts to a loss of about 5.7 million barrels a day, the kingdom’s national oil company said, roughly 5% of the world’s daily production of crude oil.