Yemen's Houthi movement said on Monday that Saudi Aramco's oil processing plants were still a target and could be attacked at "any moment", warning foreigners to leave the area.
The attacks on Aramco plants in Abqaiq and Khurais in the kingdom's eastern region were carried out by drones with normal and jet engines, Houthi military spokesman Yahya Sarea said in a tweet.
Sarea said Saudi Arabia should stop its "aggression and blockade on Yemen".
Drones attacked the world's largest oil processing facility in Saudi Arabia and a major oilfield operated by Saudi Aramco early Saturday.
Houthi rebels claimed responsibility for the attack that paralyzed production of more than half of Saudi Arabia's global daily exports and more than 5% of the world's daily crude oil production.
U.S. President Donald Trump said the U.S. was "locked and loaded" to respond to the attack that Washington has blamed on Iran as Secretary of State Mike Pompeo pointed the finger squarely at Tehran, saying there was no evidence the "unprecedented attack on the world's energy supply" was launched from Yemen.
Iranian Foreign Ministry spokesman Abbas Mousavi dismissed the U.S. allegations as "blind and futile comments."