In a Sunday evening tweet, Trump did not share the definitive accusation against Iran, instead saying the USA had "reason to believe that we know the culprit. but are waiting to hear from the Kingdom [of Saudi Arabia] as to who they believe was the cause of this attack".
Iran rejected the allegation, with a government spokesman saying now there was "absolutely no chance" of a hoped-for meeting between Iranian President Hassan Rouhani and US President Donald Trump at the UN General Assembly next week.
Al-Maliki said on Monday that the coalition has the ability to confront attacks, and defend vital oil facilities, and the results of the investigation would be made public to the media when complete.
Sunni Muslim Saudi Arabia has previously accused Shi'ite Muslim Iran, which lies across the Gulf, of carrying out attacks on its oil facilities, charges Tehran denies.
United States officials suggested to reporters that the degree of scope, precision and sophistication of the strikes was beyond the ability of Houthi rebels, even as Iran has denied responsibility and made overtures to Britain and other European nations to forestall any U.S. action.
"No matter whether it takes Saudi Arabia 5 days or a lot longer to get oil back into production, there is but one rational takeaway from this weekend's drone attacks on the Kingdom's infrastructure - that infrastructure is highly vulnerable to attack, and the market has been persistently mispricing oil, which Citi reckons should have been a good $10 a barrel higher than it has been for months", Citi analysts wrote to clients in a note.
Saudi Arabia usually ships more than 7 million bpd of oil to global destinations and has for years served as the market's supplier of last resort.
The movement has stepped up drone and missile attacks on Saudi cities this year. The attack has shaken the world's energy supply matrix and sent oil prices soaring.
Brent, the global oil benchmark, saw prices surge over 10% Monday to just shy of $67 a barrel.
The Saudi outage serves as a reminder to oil customers around the world of the political uncertainties in Middle Eastern countries, said Bob Schulz, a business professor with the Haskayne School of Business at the University of Calgary.
The US accusations triggered angry retorts from Iran, which said they were created to act as a pretext for future hostile actions against the Islamic Republic. The State Department did not immediately acknowledge what was discussed.
Oil prices are surging amid production disruptions in Saudi Arabia.
Iranian Foreign Ministry spokesman Abbas Mousavi again denied the USA claims Monday, telling journalists the accusation was "condemned, unacceptable and categorically baseless". Pompeo said Tuesday that Trump was "prepared to meet with no preconditions".
Russia's Foreign Ministry, while expressing "grave concern" about the attack, warned against putting the blame on Iran, saying that plans of military retaliation against Iran are unacceptable.
United States officials pointed to satellite imagery showing 19 points of impact on the oil facilities.
Stabilization means processing so-called sour crude oil into sweet crude.
Saudi Aramco did not respond to questions from The Associated Press regarding damage at Abqaiq and the satellite images.