Iranian state television said Iran had fired 15 missiles at US targets in Iraq early on Wednesday.
The US military said at least two Iraqi facilities hosting US-led coalition personnel were targeted at about 1:30 a.m. Iraq time (2230 GMT on Tuesday).
Iraq said 22 missiles were fired. Iranian officials said Tehran did not want a war and its strikes "concluded" its response to Friday's killing of Qassem Soleimani, a powerful general whose burial after days of mourning was completed around the time of the missile launches.
Iranian television showed mourners celebrating the attack.
US President Donald Trump said in a tweet that an assessment of casualties and damage from the strikes was under way and that he would make a statement on Wednesday morning.
"All is well!" Trump, who visited one of the targeted sites in Iraq, Ain al-Asad air base, in December 2018, said on Twitter.
All is well! Missiles launched from Iran at two military bases located in Iraq. Assessment of casualties & damages taking place now. So far, so good! We have the most powerful and well equipped military anywhere in the world, by far! I will be making a statement tomorrow morning.
— Donald J. Trump (@realDonaldTrump) January 8, 2020
One source said early indications were of no US casualties, while other US officials declined to comment.
Iranian state television said 80 "American terrorists" had been killed and US helicopters and military equipment damaged.
It did not provide evidence of how it obtained that information.
Germany, Denmark, Norway and Poland said none of their troops in Iraq were hurt. Britain, which also has personnel in Iraq, condemned the Iranian action.
Iraq said its forces did not suffer any casualties.
Pentagon spokesman Jonathan Hoffman said the bases targeted were al-Asad air base and another facility in Erbil, Iraq.
"As we evaluate the situation and our response, we will take all necessary measures to protect and defend US personnel, partners, and allies in the region," Hoffman said.
More than 5,000 US troops remain in Iraq along with other foreign forces in coalition that has trained and backed Iraqi forces against the threat of Islamic State militants.
Iran, which has long said US forces should leave the Middle East, told Washington after the attacks to withdraw its troops to prevent more deaths and warned US allies including Israel not to allow attacks from their territories.
Soleimani, a pivotal figure in orchestrating Iran's campaign to drive US forces out of Iraq, was responsible for building up Iran's network of proxy armies across the Middle East.
'Proportionate measures'
Iranian television reported an official in Supreme Leader Ali Khamenei's office as saying the missile attacks were the "weakest" of several retaliation scenarios.
It quoted another source saying Iran had lined up 100 other potential targets.
Iranian President Hassan Rouhani was expected to speak later on Wednesday, state television reported.
Hours before the Iranian strikes, US Defense Secretary Mark Esper said the United States should anticipate a response from Iran for the killing of Soleimani, commander of Iran's elite Quds Force, a unit of the Revolutionary Guards.
"I think we should expect that they will retaliate in some way, shape or form," he told a briefing at the Pentagon.
Iranian Foreign Minister Mohammad Javad Zarif said Iran "took and concluded proportionate measures in self-defense under Article 51 of the UN Charter".
"We do not seek escalation or war, but will defend ourselves against any aggression," he wrote in a post on Twitter.
Iran took & concluded proportionate measures in self-defense under Article 51 of UN Charter targeting base from which cowardly armed attack against our citizens & senior officials were launched.
— Javad Zarif (@JZarif) January 8, 2020
We do not seek escalation or war, but will defend ourselves against any aggression.
If the US military was spared casualties and Iran takes no further measures to retaliate for Soleimani's killing, there might be an opportunity for Washington and Tehran to seek a way out to their increasingly violent confrontation.
Asian stock markets, which had been roiled by the attack, pared some of their losses after the tweets from Trump and Zarif.
US crude prices also retreated after surging almost 5% on worries conflict could cut oil supplies.
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.
'Needless provocations'
Major airlines said they were re-routing flights to avoid airspace over Iraq and Iran after the Federal Aviation Administration banned US carriers from the area.
In an apparently unrelated incident, a Ukrainian airliner with more than 160 people on board crashed on Wednesday soon after taking from Tehran, killing all on board.
The Ukrainian embassy said the cause was engine failure. Democrats in the US Congress and some of the party's presidential contenders warned about the escalating conflict.
"We must ensure the safety of our service members, including ending needless provocations from the Administration and demanding that Iran cease its violence. America & world cannot afford war," US House of Representatives Speaker Nancy Pelosi said on Twitter.
Closely monitoring the situation following bombings targeting U.S. troops in Iraq. We must ensure the safety of our servicemembers, including ending needless provocations from the Administration and demanding that Iran cease its violence. America & world cannot afford war.
— Nancy Pelosi (@SpeakerPelosi) January 8, 2020
US officials 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.
The general was a national hero to many Iranians but viewed as a villain by Western governments opposed to Tehran's arc of influence running across the Levant and into the Gulf region.
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, Iranian media said.
An hour after the Iranian missile attack, its state television showed footage of Soleimani's burial, where a gathering of hundreds of people started chanting "God is greatest" when the strikes were announced over loudspeakers.
"His revenge was taken and now he can rest in peace," Iranian television 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.
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