Attacks targeting installations hosting coalition forces have 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 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.

On Wednesday evening, five rockets targeted an air base used by the coalition in western Iraq.

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

The rockets landed near the Ain Al-Asad air base in the desert of Al-Anbar province. 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 a compound attached to a US diplomatic base at the airport in Baghdad, the Iraqi capital.

Photos obtained by AFP showed remains of one of the drones with the message "commanders' revenge operations" written on it.

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.

Five days after his killing, Iran fired missiles at an air base in Iraq housing US troops and another near Arbil in the country's north.

Since then dozens of rockets and roadside bombs have targeted US security, military and diplomatic sites across Iraq.

- Syria attacks -

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 said one of its bases in northeast Syria came under fire from Iran-backed groups.

"Coalition forces were targeted this morning by eight rounds of indirect fire at Green Village" base, a statement said.

"The attack did not cause any casualties, but several rounds impacted inside the coalition base and caused minor damage."

The day before, the forces said they had foiled a rocket attack on the same base, located in a part of war-ravaged Syria under the control of Kurdish forces.

Earlier 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.

However, the coalition said it hadn't received reports of new attacks.

IS, which established a so-called caliphate across swathes of Syria and Iraq from 2014, was defeated in Iraq in 2017 by national forces and the coalition that has included more than 80 countries.

However, IS remnants still carry out attacks against security forces and civilians.