The surge of attacks targeting bases used by the coalition comes as Tehran and its Middle East allies held emotional commemorations marking the second anniversary 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.

"Our coalition continues to see threats against our forces in Iraq and Syria by militia groups that are backed by Iran," coalition chief Maj. Gen. John W. Brennan, Jr. said in a statement.

On Wednesday, 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. "No damage, no casualties."

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

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

- 'Eminently clear' -

In neighbouring Syria, the coalition said one of its bases in the northeast of the country had come under fire.

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

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

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.

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

"It remains our working level assumption that these are in fact, Iran-backed groups," Pentagon spokesman John Kirby told reporters following the attacks Wednesday.

"We've been eminently clear with Iran about how seriously we take the safety and security of our people and our mission in Iraq and Syria," Kirby added.

- 'Revenge operations' -

There has been a string of attacks on the coalition in recent days.

In Iraq, coalition forces on Monday shot down two armed drones targeting a compound attached to a US diplomatic base at the airport in the capital Baghdad.

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

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.

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.

In Syria, forces at the base attacked on Wednesday -- located in a part of the war-ravaged country under the control of Kurdish forces -- said they had also foiled a rocket attack there a day earlier.

The Britain-based Syrian Observatory for Human Rights said earlier Wednesday that 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.