Fifty percent of their output was still potentially halted on Saturday evening according to the Saudi interior ministry, and that means that 5% of world production was offline.
The attacks and recriminations are increasing already heightened fears of an escalation in the region, after a prominent USA senator suggested striking Iranian oil refineries in response to the assault, and Iran warned of the potential of more violence.
Up until just recently, it was the world's largest oil exporter.
An attack by 10 drones caused fires at a major oil processing facility and a nearby oil field in Saudi Arabia.
Tehran denies the accusations however the information has revived fears of a battle within the tinderbox Center East after a collection of assaults on oil tankers earlier this yr that have been additionally blamed on Iran.
Prior to Mr. Trump's announcement, the Energy Department said it stood "ready" to tap into the strategic petroleum oil reserves if necessary to offset any disruptions. "Consequently, the impact on oil prices and global growth is not expected to be significant or last long".
"How the United States and Saudi Arabia deal with the situation will be closely watched", said Margaret Yang, market analyst at CMC Markets in Singapore. The kingdom produces approximately 10% of the total global supply of 100 million barrels per day.
The energy minister said Aramco "is now working to recover the lost quantities" of oil and will update the public within two days.
During the weekend, the International Energy Agency stressed that global markets would not be disrupted by the Saudi attacks.
Traders and analysts said crude may spike to as high as $100 (all prices in United States dollars) a barrel if Riyadh fails to quickly bring back supply.
Amateur video of the middle-of-the night attack on the Saudi Aramco facilities in Abqaiq, in eastern Saudi Arabia, showed several blazes raging.
Trump in recent days has said that he could meet with Iran's Rouhani at the United Nations General Assembly later this month as tensions mount over the USA leader's withdrawal previous year from the 2015 worldwide pact to restrain Iran's nuclear weapons and his reimposition of economic sanctions that have hobbled Iran's economy.
Earlier, US Secretary of State Mike Pompeo claimed there was no evidence that the attack originated from Yemen.
Tweeting on Sunday, President Donald Trump stopped short of directly accusing Iran, but suggested possible military action once the perpetrator is known. Tehran ruled out talks until sanctions are lifted.
U.S. officials previously alleged at least one recent drone attack on Saudi Arabia came from Iraq, where Iran backs Shi'ite militias.
Iranian President Hassan Rouhani speaks during a cabinet meeting in Tehran, Iran, Sept. 11, 2019.