The strikes are the first in the heart of Baghdad to kill Iran-backed fighters since the start of the Middle East war on February 28, which has not spared Iraq, long a proxy battleground between the US and Iran.

"At 02:15 am (2315 GMT Friday), a missile struck a house that was being used by Kataeb Hezbollah," said a security source, adding that "a key figure was martyred," and two members of the group were wounded.

AFP journalists heard blasts in the capital followed by ambulance sirens, with witnesses saying they saw smoke rising from the Arasat neighbourhood, where several Iran-backed groups are known to be present.

Two hours later, an airstrike hit a vehicle in eastern Baghdad that killed "a member of the Hashed al-Shaabi," another security source said.

A Hashed al-Shaabi official told AFP the member killed belongs to Kataeb Hezbollah.

The Hashed al-Shaabi, or the Popular Mobilisation Forces (PMF), is a former paramilitary group now integrated into the regular armed forces.

It also encompasses brigades from Iran-backed groups, including Kataeb Hezbollah.

None of the sources said who was believed to be behind the strikes, and the Kataeb Hezbollah group has not commented.

But since the start of the war, several attacks that targeted Iran-backed fighters across Iraq have been blamed on the US and Israel.

The US designates several Tehran-backed Iraqi armed groups as terrorist organisations.

These groups are also united under an alliance called the Islamic Resistance in Iraq, which have been claming daily drone and rocket attacks against US bases in Iraq and the region.