A military spokesman said that Iran was "ready for a fully-fledged war".
Iran has warned the U.S. that its bases and aircraft carriers are within range of its missiles after Tehran was blamed for drone attacks on two oil refineries in Saudi Arabia.
The attacks on Saturday—which knocked out half of Saudi Arabia's oil output and caused massive fires—were claimed by Yemen's Houthis, a rebel group aligned with Iran and currently fighting a war against the Saudi-led coalition which has seen a spate of similar attacks.
But U.S. Secretary of State Mike Pompeo blamed Tehran late on Saturday, arguing that there was "no evidence" that the attacks came from Yemen.
A commander in Iran's revolutionary guard hit back on Sunday, warning that U.S. bases within 2,000 kilometres of the country were "within range of our missiles". He was also quoted as saying that Iran "has already been ready for a fully-fledged war."
Later, Iranian foreign ministry spokesman Abbas Mousavi, speaking on state TV, dismissed the U.S. claim as "pointless".
The attacks, which took place early on Saturday, caused huge fires that were later extinguished by the Saudi authorities, a Saudi interior ministry spokesman said. The attacks also cut about 50% of the company's crude oil output, the energy minister said in a statement, according to Reuters.
UK foreign secretary Dominic Raab weighed in after speaking with his US counterpart.
He called the attack a "reckless attempt to damage regional security and disrupt global oil supplies."
"The UK condemns such behaviour unreservedly," he added.
Yemeni TV channel al-Masirah said the Houthis had deployed 10 drones against the sites in Abqaiq and Khurais, and the group pledged to widen the range of its attacks on Saudi Arabia.
Abqaiq, 60 km (37 miles) southwest of Dhahran in Saudi Arabia’s Eastern Province contains the world’s largest oil processing plant and Khurais, 190 km further southwest, contains the country’s second-largest oilfield.
Tensions are running high in the region after attacks in June and July on oil tankers in Gulf waters that Riyadh and Washington blamed on Iran. Tehran denies the accusations.
Iran-aligned Houthi fighters have also launched attacks over the border, hitting Shaybah oilfield with drones last month and two oil pumping stations in May. Both attacks caused fires but did not disrupt production.
Security forces foiled an al Qaeda attack on Abqaiq in 2006.
US Senator Chris Murphy, a Democrat on the Senate Foreign Relations Committee, called Pompeo's tweet an "irresponsible simplification".
"The Saudis and Houthis are at war. The Saudis attack the Houthis and the Houthis attack back. Iran is backing the Houthis and has been a bad actor, but it’s just not as simple as Houthis=Iran," Murphy tweeted.
Aramco is preparing to float shares as early as this year as part of efforts to diversify the economy of the world’s top oil exporter away from crude. It has hired nine banks as joint global coordinators to lead the IPO and has been meeting bankers this week in Dubai as it speeds up the listing plans.