The group, Saraya Awliya Al-Dam, is one of a group of Shiite militias operating in Iraq following the 2003 US-led invasion of the country that toppled Saddam Hussein.
The US and Iraq did not immediately comment on the claim.
The attack comes as Iranian-supported militias including the Lebanese group Hezbollah have entered the war started by the US and Israel launching an airstrike campaign targeting Iran’s theocracy.