Riyadh, which is bogged down in a five-year war against Tehran-aligned rebels in neighbouring Yemen, has said that the weapons used were Iranian-made, but has not directly blamed its arch rival.
However, the Saudi defence ministry said its spokesman would present evidence from the site of the weekend attacks that halved Saudi oil production, sending global energy markets into a tailspin.
He "will announce the final results of the investigation and present material evidence and Iranian weapons proving the Iranian regime’s involvement in the terrorist attack," the ministry said.
Late Tuesday, Energy Minister Prince Abdulaziz bin Salman said international investigators, including from the UN, were joining the probe, having announced that output would return to normal by the end of the month.
The kingdom wants "proof based on professionalism and internationally recognised standards," he said.
The Saudis will present the evidence ahead of Pompeo's arrival.
The US chief diplomat is set to meet with de facto Saudi ruler Crown Prince Mohammed bin Salman to discuss how to respond to the strikes, which the US says originated in Iran.
"As the president said, we don't want war with anybody, but the United States is prepared," Vice President Mike Pence said in a speech in Washington on Tuesday.
"We're locked and loaded and we're ready to defend our interests and allies in the region, make no mistake about it," he said, echoing President Donald Trump's words on Sunday.
A US official, speaking on condition of anonymity, told AFP that the Trump administration has concluded that last weekend's attack involved cruise missiles from Iran and that evidence would be presented at the UN General Assembly next week.
Prefer not to meet
The apparent hardening of the US position came as Iran's supreme leader Ayatollah Ali Khamenei ruled out negotiations with Washington "at any level".
This appeared to nix remaining hopes for a dramatic meeting between Trump and Iranian President Hassan Rouhani at the United Nations next week.
Speaking to reporters on Air Force One over California, Trump said he too had cooled on what had always seemed to be a diplomatic longshot.
"I never rule anything out, but I prefer not meeting him," Trump said.
Yemen's Huthi rebels claimed responsibility for Saturday's oil installation attacks, which took out six percent of global supplies.
But a senior US administration official cast doubt on that claim, saying that while the Huthis said they used 10 drones, one Saudi oil facility was hit "at least 17 times," and another twice by "precision-guided munitions."
Additionally, neither the type of drone "nor the cruise missiles employed in the attack can reach the facilities from Yemen. It's not possible," the official said.
The Huthis are at war with Saudi-backed forces in Yemen, turning the impoverished nation into a proxy battlefield for Tehran and Riyadh.
Observers say the torrid experience in Yemen, where despite their vast firepower, the Saudis have failed to subdue the ragtag but highly motivated militia, has made Riyadh circumspect about wading into another conflict.
"I certainly hope we're not (going to have another war)," Riyadh's ambassador to London Prince Khalid Bin Bandar told the BBC in an interview.
"Almost certainly it's Iranian-backed, but we are trying not to react too quickly because the last thing we need is more conflict in the region," he said.
Iran has stuck with its account that the Huthi rebels are responsible, with Rouhani saying Wednesday that they carried out the strike as a "warning" about a possible wider war in response to the Saudi intervention in Yemen.
Support for war?
The increasingly complex conflict dovetails with the Trump administration's attempt to curb Iranian power through a "maximum pressure" campaign of crippling economic sanctions.
Trump began that campaign after unilaterally pulling out of a 2015 international deal meant to reward Iran for allowing restrictions on its nuclear industry.
The new stage of the long-running US-Iranian standoff has raised speculation over whether it will lead to conflict.
Trump called off a retaliatory missile attack on Iran in June after the Iranians shot down a spy drone.
He said he did not want to kill what generals told him could be up to 150 people.
Trump's administration is considering responses to the latest attack, including a cyber attack or a physical strike on Iranian oil infrastructure or its Revolutionary Guards, NBC News reported, citing unnamed US officials.
Oil prices have see-sawed since the attacks, with record gains Monday followed by a tumble Tuesday as the Saudi assurances on supply soothed the markets.