The Ain al-Asad airbase was targeted by the attack, which is located in the western Iraqi province of Anbar. The rockets struck the airbase at 7.20am local time (4.20am GMT) on Tuesday, Colonel Wayne Marotto, a spokesman for the US-led coalition forces in the country, said on Twitter.
A Baghdad Operations Command official told Reuters news agency about 13 rockets were launched from a location about 8km (5 miles) from the base.
Another Iraqi security source said the rockets were launched from the Baiader area.
No one was injured in the attack and it is not yet clear who was behind the strike.
The attack on the Ain al-Assad base in Iraq’s western desert comes after several weeks of escalating US-Iran tensions on Iraqi soil.
On February 26, US President Joe Biden authorised an airstrike on an Iran-backed Shia militia compound in neighbouring Syria.
The US military dropped seven 500-pound Joint Direct Attack Munitions (JDAMs), which reportedly killed 22 at a crossing used by Iranian-backed militia groups to move weapons across the border.
The President said the airstrike he ordered was a warning to Iran to “be careful” and not support militia groups that threaten Americans.
Pentagon spokesman John Kirby said: “At President Biden’s direction, U.S. military forces… conducted airstrikes against infrastructure utilised by Iranian-backed militant groups in eastern Syria.”
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The attack killed one contractor, who was not American, and injured numerous American contractors and an American service member, as well as Iraqi civilians.
Just days after the February 15 attack, a salvo struck a base north of Baghdad hosting American forces and injured at least one contractor.
Yesterday’s rocket attack comes just days before Pope Francis is due to visit Iraq.
The 84-year-old is due to arrive in Baghdad on Friday and will mark the first ever papal visit to Iraq.
Pope Francis’s visit will start will a ceremony at the presidential palace and a meeting with President Barham Salih and prime minister Mustafa al-Kadhimi.
The pontiff will also meet bishops, priests and others at the city’s Syro-Catholic Cathedral of Our Lady of Salvation.
He will then travel south to the holy city of Najaf to meet the Grand Ayatollah Ali al-Sistani, the influential 90-year-old Shia Muslim cleric.
The Iraqi government has promised high security during the three-day visit to six cities.