The attack on Saudi Arabia's oil facilities originated from inside Iran, according to US media reports.
It comes as the Saudi energy minister announced that half of the crude oil production cut after the attack had been restored.
The remainder will be fully restored by the end of the month, said Prince Abdulaziz bin Salman.
Production capacity will be increased to 11 million barrels per day by the end of September, he said. It was around 9.6 million barrels per day before the attack.
Meanwhile, news agency Reuters quoted a US official as saying last week's attack had used cruise missiles and drones originating in Iran's southwest.
An NBC report cited two US officials as saying a series of low-altitude cruise missiles were fired from at least one location in the west of the country.
The Abqaiq facility and the Khurais oil field were attacked in the early hours of Saturday, causing a reduction of more than half in Saudi Arabia's daily oil exports - more than 5% of the world's daily production.
Houthi rebels, who are backed by Iran in the devastating civil war in Yemen, have said they were responsible.
A Saudi-led coalition has been fighting the Houthis in Yemen, which borders Saudi Arabia.
Iranian foreign minister, Mohammad Javad Zarif, said on Twitter that the US was "in denial if it thinks that Yemeni victims of 4.5 yrs of the worst war crimes wouldn't do all to strike back".
"Perhaps it's embarrassed that $100s of blns of its arms didn't intercept Yemeni fire. But blaming Iran won't change that."
Also on Tuesday, Saudi media minister Turki bin Abdullah Al-Shabanah said the attacks were aimed at "threatening international peace and security and global energy supplies and is an extension of previous acts of aggression on Saudi Aramco's pumping stations involving the use of Iranian weapons".
He added: "[Saudi] cabinet members called on the international community to shoulder its responsibility in condemning those behind these egregious attacks."
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US Vice President Mike Pence has echoed Donald Trump's earlier words, saying America is "locked and loaded" should military action become necessary.
He tweeted: "In the wake of this weekend's unprovoked attack on several oil facilities in Saudi Arabia, I promise you: We're ready."
Shortly after the attacks, Mr Trump said the US could release some of its oil reserves if needed.
However, he has now said he does not think it is necessary as prices have not risen very much.
Prices soared nearly 20% on Monday, eventually settling up 14%, but Brent crude dropped by more than 5% ahead of the Saudi oil minister's speech - to around $65 - and were trading at $64 on Wednesday morning.