Pentagon spokesman Jonathan Hoffman confirmed the Ain Asad air base and another facility in Erbil were targeted in the attack at about 1.30am (9.30am AEDT).
Reports of casualties vary wildly. One source said early indications were of no US casualties, while other US officials declined to comment.
Iranian state television claimed 80 “American terrorists” had been killed and US helicopters and military equipment damaged. It did not provide evidence of how it obtained that information.
On Twitter, US President Donald Trump said initial assessments of were: “So far, so good!”.
“All is well!” Trump, who in December 2018 visited one of the targeted sites in Iraq, Ain Asad air base, tweeted.
While some analysts predicted a US response to the attack, no action had been taken at the time of writing.
A bullish Republican Senator Lindsey Graham, speaking on Fox News in the US following the incident, said he had “just got off the phone” with Trump and said if Iran continues with “this crap” they are “going to wake up one day out of the oil business.”
“This was an act of war, Sean, by any reasonable definition,” Graham continued, before declaring that “the President has all the authority he needs under Article II to respond. How he responds is yet to be determined.”
Iran’s Revolutionary Guards advised the United States to withdraw its troops from the region to prevent more deaths and warned US allies including Israel not to allow attacks from their territories.
A day earlier, Iraq’s outgoing Prime Minister Adel Abdul-Mahdi reiterated his plea for US troops to leave the country after the nation’s parliament held a successful vote to that effect.
Prime Minister Scott Morrison said he had been told all Australian diplomatic and defence personnel in Iraq were safe but he warned the situation was “very fluid” and the government was in contact with the Trump administration.
Iranian television reported an official in the office of Supreme Leader Ayatollah Ali Khamenei as saying the missile attacks were the “weakest” of several retaliation scenarios. It quoted another source saying Iran had 100 other potential targets in its sights.
Asian stock markets, which had been roiled by the attack, pared some of their losses after the tweets from Trump. US crude prices also retreated after surging almost 5 per cent on worries any conflict could cut oil supplies.
Suhail Mazrouei, the oil minister of the United Arab Emirates, a member of the Organisation of the Petroleum Exporting Countries, said the latest events should not be exaggerated. He said there was no global crude shortage and OPEC would respond to any need.
The US Federal Aviation Administration said it would ban US airlines from operating in the airspace over Iraq, Iran, the Gulf and the Gulf of Oman. Other national airlines also issued warnings about flying over the region.
Australian airline Qantas confirmed on Wednesday it would also reroute flights to avoid airspace near Iran.
In an apparently unrelated incident, a Ukrainian airliner carrying more than 160 people crashed in Iran on Wednesday, killing all those on board, due to technical problems soon after taking off from Tehran’s Imam Khomeini airport, Iranian media and Ukrainian officials said.
Qassem Soleimani, whose killing last week raised fears of a wider war in the Middle East, was a pivotal figure in orchestrating Iran’s long-standing campaign to drive US forces out of Iraq. He was responsible for building up Tehran’s network of proxy armies across the Middle East.
He was a national hero to many Iranians but viewed as a dangerous villain by Western governments opposed to Iran’s arc of influence running across the Levant and into the Gulf region.
US officials have said Soleimani was killed because of intelligence indicating forces under his command planned attacks on US targets in the region, but they have not provided evidence.
Before Soleimani was buried his body was taken on a tour of cities in Iraq and Iran, drawing huge crowds, often chanting “Death to America”.
His burial on Tuesday was delayed after a stampede that killed at least 56 people, Fars news agency reported.
Iran TV reported Soleimani was buried after the Iranian missile attacks. “His revenge was taken and now he can rest in peace,” it said.
The missiles were launched on Wednesday at the same time of the day that he was killed on Friday. He was buried in the “martyrs section” of a cemetery in his hometown of Kerman.
More than 5000 US troops remain in Iraq along with other foreign forces as part of a coalition that has trained and backed up Iraqi security forces against the threat of Islamic State militants.
with Reuters, AP