RNA - The IRGC announced in a statement on Friday morning that Major General Soleimani and al-Muhandis were martyred in the attack carried out by US helicopters.
The Iraqi pro-government group also confirmed the incident.
"The deputy head of the Hashed, Abu Mahdi al-Muhandis, and head of the Quds Force, Qasem Soleimani, were killed in a US strike that targeted their car on the Baghdad International Airport road," it a statement on Friday.
"The American and Israeli enemy is responsible for killing the mujahideen Abu Mahdi al-Muhandis and Qassem Soleimani," said Ahmed al-Assadi, a PMU spokesman.
The group had earlier said that its public relations director Mohammed Reza al-Jaberi and four other members of the group were also killed after three Katyusha rockets struck a military base next to Baghdad International Airport in the Iraqi capital.
The media bureau of the voluntary forces – better known by the Arabic word Hashd al-Shabai – described the early Friday morning attack as a "cowardly US bombing”.
The rockets landed near the air cargo terminal, burning two vehicles and injuring several people, the Iraqi Interior Ministry's Security Media Cell said in an earlier statement.
Meanwhile, security sources, speaking on condition of anonymity, told AFP that eight people were killed in the attack.
The development came as the United States military said on Sunday it had carried out strikes in western Iraq against Kataib Hezbollah group, which is part of the pro-government Popular Mobilization Units – better known by the Arabic word Hashd al-Sha’abi.
Iraqi security sources said at least 25 fighters were killed and at least 55 wounded following the air attacks.
Senior Iraqi officials also condemned the US attack against the Kataib Hezbollah's positions as a "violation of Iraqi sovereignty".
Caretaker Iraqi Prime Minister Adel Abdul Mahdi called the move a “dangerous escalation that threatens the security of Iraq and the region” in a statement on Sunday,
Iraqi caretaker President Barham Salih also condemned the attack.
The US raids drew a wave of condemnation from officials and movements across the region, and triggered furious public protests outside the US embassy in Baghdad.