"We observed five rounds... the closest impact was two kilometres (1.2 miles) away," a coalition official said. "No damage, no casualties."

The rockets landed near the Ain Al-Asad air base in western Iraq, in the desert of Al-Anbar province.

The coalition uses the base in its fight against the Islamic State group.

The same base was targeted on Tuesday, when US-led coalition forces shot down two armed drones.

On Monday, the coalition also shot down two armed drones targeting its compound at the airport in Baghdad, the Iraqi capital.

The attacks targeting US installations come as Tehran and its allies across the Middle East held emotional commemorations marking the second anniversary on Monday of the assassination of Iranian commander General Qasem Soleimani and his Iraqi lieutenant in a US drone strike at Baghdad airport.

The January 3, 2020 strike, ordered by then-US president Donald Trump, hit a car in which Soleimani and Abu Mahdi al-Muhandis were travelling on the edge of the airport.

The US said at the time that Soleimani was planning imminent action against US personnel in Iraq, a country long torn between the competing demands of its principal allies Washington and Tehran.

Western officials have blamed hard-line pro-Iran factions for the attacks, which have never been claimed.

The Hashed al-Shaabi -- a coalition of former paramilitary groups now integrated into the Iraqi state security apparatus --- has repeatedly called for the withdrawal of US troops deployed in Iraq as part of the coalition.

Muhandis was deputy leader of the Hashed at the time of his killing.

Coalition troops switched to a training and advisory role with the end of their combat mission in Iraq early last month.

Also on Wednesday, the coalition also said one of its bases in northeast Syria came under fire from Iran-backed groups.

The development came one day after the forces said they had foiled a rocket attack on the same Syrian base, located in a part of war-ravaged country under the control of Kurdish forces.

Earlier on Wednesday, the Britain-based Syrian Observatory for Human Rights said pro-Iran militia fighters fired shells towards a US base in eastern Syria's Al-Omar oil field, causing damage but no casualties.