Iraqi military bases hosting US troops in Iraq’s western Anbar province and the capital Baghdad were hit by Katyusha rockets on Wednesday.
And in Syria, eight rounds of indirect fire landed inside a base with members of the US-led coalition, the Iraqi and US militaries said.
No casualties were reported in the three attacks, part of a series that began on Monday, the anniversary of a US air strike that killed top Iranian general Qassem Suleimani in Baghdad two years ago.
An Iraqi officer said a base housing US troops in the western Anbar province was hit with five Katyusha rockets on Wednesday evening. Three other rockets fell outside the base’s perimeter.
The officer said US-led coalition forces at the base were forced into shelters by the barrage.
There was no immediate comment from the coalition, which is in Iraq to help fight ISIS.
Later Wednesday, a previously unheard-of group in Iraq calling itself Qassem Al Jabarayn claimed responsibility for the Ain Al Asad attack.
The group pledged in an online post to keep up attacks until the full withdrawal of US forces.
Since Suleimani’s death, Iran-backed militias in Iraq have become increasingly unruly and disparate, although some analysts say they have splintered only to allow them to claim attacks under different names to hide their involvement.
Earlier on Wednesday, the Iraqi military said a rocket launcher with one rocket was found in a residential district in western Baghdad, an area used in the past by Iran-backed militias to fire at the airport.
In eastern Syria, the rounds hit a base run by the US-backed Syrian Democratic Forces with a small coalition advisory presence. The coalition said there was minor damage.
Coalition forces, acting on intelligence, responded by firing six rounds of artillery towards the point of origin of the attack just outside the eastern town of Mayadeen, a stronghold of Iran-backed fighters, the coalition said.
“Iran-supported malign actors fired … from within civilian infrastructure with no regard for civilian safety,” it said.
The coalition said that hours earlier, US-led coalition forces had watched several launch sites near the base known as Green Village.
Coalition forces conducted strikes to eliminate the threats, it said.
“The coalition reserves the right to defend itself and partner forces against any threat, and will continue to do everything within its power to protect those forces,” said Maj Gen John Brennan, commander of the joint task force.
Pentagon spokesman John Kirby said on Wednesday that the military has been preparing for increased attacks in Iraq around the end of the year.
“We’re very mindful of the threat environment and it is very dynamic right now,” Mr Kirby said.
He said the attacks could be related to the anniversary of Suleimani’s killing or a reaction to the continuing presence of American forces in Iraq, but are probably a combination of both.
Iranian-backed militias have wanted all US troops out of the country, and many believed that would happen by the end of the year.
On Monday, two armed drones were shot down as they headed towards a centre housing US advisers at Baghdad airport.
Two explosives-laden drones targeting an Iraqi military base housing US troops in western Anbar province were destroyed on Tuesday.
The 2020 US drone strike at Baghdad’s airport killed Suleimani, who was the head of Iran’s overseas operations branch, the Quds Force, and Abu Mahdi Al Muhandis, deputy commander of Iran-backed militias in Iraq known as the Popular Mobilisation Forces.
Pro-Iran factions in Iraq have vowed revenge for the killing and have said attacks against the US presence in Iraq would stop only when American troops leave the country.
The US-led coalition formally ended its combat mission supporting Iraqi forces in the continuing fight against ISIS last month.
About 2,500 troops will remain as the coalition shifts to an advisory mission to continue supporting Iraqi forces.
The top US commander for the Middle East, Gen Frank McKenzie, warned last month that he expected increasing attacks on US and Iraqi personnel by Iranian-backed militias.