Three rockets targeted an Iraqi air base hosting American troops on Monday without causing casualties, a spokesman for the US-led coalition said.

Colonel Wayne Marotto, a spokesman for the international coalition in Iraq, said on Twitter that the Ain al-Assad base "was attacked by three rockets" in the early afternoon.

"The rockets landed on the base perimeter. There are no injuries and damage is being assessed," he said.

The assault on the Ain al-Assad facility in the western province of Anbar is the latest in a series of attacks on American interests in Iraq which Washington blames on Iran-linked militias.

US forces, whose 2,500 troops are deployed in Iraq as part of an international coalition to fight the jihadist Islamic State group, have been targeted more than 40 times this year.

There was no immediate claim of responsibility for Monday's attack, which came a week after deadly US air strikes on pro-Iran fighters in both Iraq and Syria.

The Pentagon said the raids were retaliation for attacks on US interests, and Secretary of State Antony Blinken declared they sent a "strong message" not to keep attacking American forces.  

The Hashed-al-Shaabi, an Iraqi paramilitary alliance that includes several Iranian proxies and has become the main power broker in Baghdad, said the raids killed four of its fighters in the Qaim region near the border with Syria.

The June 27-28 overnight strikes targeted operational and weapons storage facilities at two locations in Syria and one in Iraq, the Pentagon said.

Hours later, pro-Iran militias fired several shells at an American base in eastern Syria.

Iran-aligned groups operate in Iraq, which counts both Tehran and Washington as allies, and in war-torn Syria, where Iran is a key backer of the Damascus regime.