The attack threatens a dangerous escalation, with suspected US-led coalition airstrikes promptly targeting Iran-aligned Iraqi fighters in neighbouring Syria, a war monitor said. At least 18 fighters were reported killed.
On Wednesday evening, a volley of 18 Katyusha rockets hit the Taji air base north of Baghdad which hosts troops from the US-led coalition helping local forces battle.
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A coalition statement said three of its personnel were killed and another 12 were wounded but it did not provide nationalities.
A US official, however, told AFP the dead included two Americans and a British national.
The Iraqi military said the rockets were fired from the back of a truck, but it did not comment on any casualties.
US Secretary of State Mike Pompeo and British Foreign Minister Dominic Raab condemned the attack in a telephone call.
The two "underscored that those responsible for the attacks must be held accountable," the US State Department said in a statement.
While there was no immediate claim of responsibility, Washington has blamed Iran-backed factions from Iraq's Hashed al-Shaabi military network, which is incorporated into the Iraqi state, for recent similar violence.
Within hours of Wednesday's attack, three warplanes likely belonging to the US-led coalition bombed Hashed factions stationed on the Syrian side of the border with Iraq, according to the Syrian Observatory for Human Rights war monitor.
At least 18 Iraqi fighters were killed as "ten explosions shook the area near Albukamal," a Syrian border town with a heavy Hashed presence, said Observatory head Rami Abdel Rahman.
Hardline Hashed factions have fought alongside Syrian government forces for several years and have been targeted by both coalition and Israeli airstrikes in Syria.
Wednesday's attack on the Taji airbase was the 22nd on US installations in Iraq, including the American embassy, since late October.
One of the earlier attacks killed an Iraqi soldier and in late December, a spree of rockets killed a US contractor working at a base in northern Iraq.
That killing sent tensions spiralling.
Two days later, the US responded by bombing Kataeb Hezbollah, a faction within the Hashed that is heavily backed by Iran and which Washington has blamed for several rocket attacks.
At least 25 Kataeb Hezbollah fighters were killed and their supporters on 31 December besieged the US embassy in Baghdad.
A US drone strike outside the Baghdad airport on January 3 killed powerful Iranian military commander Qasem Soleimani and the Hashed's deputy chief Abu Mahdi al-Muhandis.
Iran then retaliated by launching a volley of missiles at the western Iraqi base of Ain Al-Asad. While no personnel were killed in that attack, dozens of US soldiers suffered from brain trauma.
The tit-for-tat attacks on Iraqi soil left Baghdad furious, and in January its parliament voted to expel all foreign soldiers from Iraq in reaction to the killing of Soleimani.
Among them are some 5,200 US forces stationed across Iraq as part of the international coalition -- comprised of dozens of countries -- formed in 2014 to confront the militant Islamic State group, which took swathes of territory that year.
While militant IS has lost its territory, sleeper cells remain capable of carrying out attacks.
On Sunday, two US soldiers were killed while helping Iraqi forces battle IS remnants north of Baghdad.
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Parliament's vote on the ouster must be implemented by the government, but the current caretaker cabinet has yet to make progress on the decision.
US officials previously told AFP they considered the Hashed as a bigger threat to them than IS, given the frequency and accuracy of rocket attacks on American troops that could be traced back to the Shiite-majority network.
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