He dismissed a claim by Yemen’s Iran-backed Houthi rebels that they had attacked the two facilities, run by state-owned company Aramco.
Iran’s foreign minister accused Mr Pompeo of “deceit”.
Saudi Arabia’s energy minister said the strikes had reduced crude oil production by 5.7 million barrels a day – about half the kingdom’s output.
Correspondents say they could have a significant impact on world oil prices.
The main Saudi stock exchange plummeted 3% on opening on Sunday, before recovering.
Saturday’s drone attacks hit Abqaiq, site of Aramco’s largest oil processing plant, and the Khurais oilfield.
The Saudis lead a Western-backed military coalition supporting Yemen’s government, in opposition to the Houthi rebel movement.
The attacks also come against a backdrop of continuing tension between the US and Iran, following US President Donald Trump’s abandonment of a deal limiting Iran’s nuclear activities and reinstatement of sanctions.
What did Mike Pompeo say?
In a tweet, he said there was “no evidence” the drones came from Yemen.
He described the attack as “an…