The US bombed the headquarters of the Iran-backed Iraqi Hezbollah group in Iraq and Syria, the Pentagon said Sunday, after a series of attacks in Iraq against American interests.

The attack came after a barrage of 30 or more rockets was fired on Friday at the K1 Iraqi military base in Kirkuk, an oil-rich region north of Baghdad, killing a US civilian contractor and wounding four US service members as well as Iraqi security forces, the Pentagon said, according to AFP.

Repeated mortar and rocket attacks have since late October targeted American interests in the country, where the US has 5,200 troops deployed as part of the international coalition against the Islamic State (ISIS) jihadist group.

US officials said that Washington believes Iran is behind the series of increasingly sophisticated rocket attacks.

"In response to repeated Kata'ib Hizbollah (KH) attacks on Iraqi bases that host... coalition forces, US forces have conducted precision defensive strikes against five KH facilities in Iraq and Syria," a Pentagon spokesman said in a statement on Sunday, according to AFP.

The strikes against three locations in Iraq and two in Syria "will degrade KH's ability to conduct future attacks" against coalition forces, the statement added.

"KH has a strong linkage with Iran's Quds Force and has repeatedly received lethal aid and other support from Iran that it has used to attack" coalition forces, the Pentagon said, referring to the external arm of Iran's Revolutionary Guards.

An Iraqi military official told AFP that seven members of the pro-Iran Hashed al-Shaabi paramilitary group had been killed in the US attacks, including a senior commander.

The Iraqi high command meanwhile said the US strikes hit the western Anbar province which borders Syria and that 30 fighters had also been wounded.

Friday's attack on the K1 base in Kirkuk involved a direct hit on an ammunition depot caused secondary explosions, and four more rockets were found in their tubes in a truck at the launch point, according to a US official who spoke on condition of anonymity.

Federal security forces, Shiite militia units and ISIS sleeper cells all have a presence in Kirkuk province, which is claimed by both Iraq's autonomous Kurdistan Region and federal authorities.

The recent tensions come amid US accusations that Iran has been moving short-range ballistic missiles into Iraq.

A report last year said that Iran had transferred short-range ballistic missiles to its Shiite allies inside Iraq.

Iran rejected the report, claiming it aimed to harm Iran’s ties with its neighbors. Iraq’s Foreign Ministry said the article was “without evidence”, though it stopped short of denying its contents.