The Tehran-backed Huthi rebels in neighbouring Yemen, where a Saudi-led coalition is bogged down in a five-year war, claimed Saturday's strikes on two plants owned by state energy giant Aramco.
But US 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.
"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 US diplomat added.
That drew an angry response from Tehran, where foreign ministry spokesman Abbas Mousavi said: "Such fruitless and blind accusations and remarks are incomprehensible and meaningless."
The remarks were designed to damage Iran's reputation and provide a pretext for "future actions" against the Islamic republic, he added.
Baghdad, caught between its two main sponsors -- Tehran and Washington -- also denied any link to the attacks amid media speculation that the drones were launched from Iraq.
Saudi de facto ruler Crown Prince Mohammed bin Salman, whose nation is pitted against Iran in a decades-long struggle for regional dominance, has said the kingdom is "willing and able" to respond to this "terrorist aggression".
But a tit-for-tat strike on Iranian oil fields is "highly unlikely", Middle East expert James Dorsey told AFP.
"The Saudis do not want an open conflict with Iran. The Saudis would like others to fight that war, and the others are reluctant," said Dorsey, from the S. Rajaratnam School of International Studies in Singapore.
- Markets nervous -
Instead, the kingdom focused on restoring production at the plants, as the Saudi bourse slumped three percent when the week's trading began on Sunday morning.
Saturday's explosions set off fires that engulfed the Abqaiq plant, the world's largest oil processing facility, and nearby Khurais, which hosts a massive oil field.
Saudi's energy infrastructure has been hit by the Huthis many times before, but this strike was of a different order, abruptly halting 5.7 million barrels per day (bpd) or about six percent of the world's oil supply.
"The genie is out of the bottle," said Bill Farren-Price, director of the London-based RS Energy Group.
"It is now clear that Saudi and other Gulf oil facilities are vulnerable to this kind of attack, which means that the geopolitical risk premium for oil needs to rise."
No casualties were reported but the full extent of the damage was not clear, nor the type of weapons used, and reporters were kept away from the plants amid beefed-up security.
A significant volume of oil production can be restored within days but Aramco would need weeks to reach full output again, Bloomberg News reported Sunday, citing unnamed sources.
Aramco has said it will dip into its reserves to offset the disruption, but the incident could affect investor confidence as its stock market debut looms.
As markets closely watch Saudi's ability to get its industry back on track, Aramco CEO Amin Nasser said Saturday that "work is underway" to restore production.
And newly appointed Energy Minister Prince Abdulaziz bin Salman said part of the drop would be offset by drawing on vast storage facilities designed to be tapped in times of crisis.
- Loggerheads -
Following a phone call between US President Donald Trump and Prince Mohammed, the White House condemned the attacks on "infrastructure vital to the global economy".
Tehran and Washington have been at loggerheads since May last year, when Trump pulled the US out of a landmark 2015 deal with world powers that promised Iran relief from sanctions in return for curbs on its nuclear programme.
Despite the US accusation, the White House said on Sunday Trump may still meet his Iranian counterpart Hassan Rouhani at the upcoming United Nations assembly.
The attacks drew condemnation from UN Secretary-General Antonio Guterres, who urged all parties to exercise "maximum restraint", as well as from the Organisation of Islamic Cooperation, a 57-member pan-Islamic body.
Britain, France, Germany and Riyadh's main Gulf allies including the UAE also criticised the attack.
Saudi Arabia has spent billions on military hardware but recent events have underscored the vulnerability of its infrastructure to attack.
In recent months, the Huthis have staged repeated cross-border missile and drone attacks targeting Saudi air bases and other facilities in what they say is retaliation for the Riyadh-led bombing campaign on rebel-held areas in Yemen.
