The attacks are unlikely to change plans for Aramcos long-awaited initial public offering but may affect the valuation, risk consultancy Eurasia Group said in a note.
Trump offered Prince Mohammed "his support for Saudi Arabia's self-defence", the White House said, following an earlier statement from Riyadh saying the crown prince told Trump the kingdom was "willing and able" to respond to the attacks blamed on Yemeni rebels".
President Donald Trump on Sunday telephoned Saudi Crown Prince Muhammad Bin Salman after attacks on two Saudi Aramco plants, including the world's biggest oil processing facility.
Tensions between the US and Iran have escalated in recent months, since US President Donald Trump abandoned a deal limiting Iran's nuclear activities a year ago and reinstated sanctions.
While markets remain closed Sunday, the attack could shock world energy prices.
No group has yet claimed responsibility for the attack; however, Saudi-led coalition now fights against the Houthi rebels in Yemen, who carried out similar attacks in the past.
The attacks not only target the Kingdom's vital installations, but also target the global oil supply and threaten its security, he said, and are a threat to the world economy.
"The United States will work with our partners and allies to ensure that energy markets remain well supplied and Iran is held accountable for its aggression", the top USA diplomat added.
Also on Sunday, Iran's foreign ministry dismissed the U.S. accusations as "meaningless", suggesting they were a pretext to retaliate against the Islamic Republic.
France, condemning Saturday's attack, said such actions "can only worsen regional tensions and risk of conflict".
But the full extent of the damage was not immediately clear as reporters were not allowed near the plants where Saudi authorities swiftly beefed up security. "This is one of the biggest central processing facilities in the world".
Oil prices could rise by as much as $10 per barrel after the weekend.
The Iran-aligned Houthi rebel movement has been fighting the Yemeni government and a Saudi-led coalition.
In addition, Saudi Arabia led airstrikes have led to deaths of scores of civilians, in the war-ravaged country since 2015.
Mr Sarea, the Houthi group's military spokesman, told al-Masirah that operations against Saudi targets would "only grow wider and will be more painful than before, so long as their aggression and blockade continues".
Tension in the vital shipping lanes worsened when Iran shot down a United States surveillance drone over the Strait of Hormuz in June, leading a month later to the Pentagon announcing the deployment of USA troops to Saudi Arabia.
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