Supporters of Hashed al-Shaabi, an Iraqi paramilitary network dominated by Iran-backed factions, Saturday burned down the main Kurdish party's headquarters in Baghdad after criticism from a Kurdish ex-minister.

Hundreds of Hashed demonstrators swept past a security detail and stormed into the offices of the Kurdistan Democratic Party (KDP), which runs the Kurdish autonomous region in northern Iraq, and torched them.

Protesters burned Kurdish flags while others carried posters of Iranian general Qasem Soleimani and his Iraqi lieutenant Abu Mahdi al-Muhandis, who were killed in a US drone strike in Baghdad last January. The Hashed paramilitaries were formed in 2014 from mostly-Shiite armed groups and volunteers to fight the Islamic State jihadist group.

Hashed has since been formally integrated into Iraq's armed forces and has representation in parliament, and it has spawned several ideologically affiliated armed groups. Earlier this month, Hoshyar Zebari, Iraq's longtime former foreign minister and a key Kurdish power-broker, said the government needed to "clean up the Green Zone (in Baghdad) from the presence of Hashed militias".

They were operating "outside the law", Zebari, a KDP member, said in comments to the US-funded Al-Hurra television. Vian Sabry, head of the KDP bloc in parliament, condemned Saturday's attack.

"This isn't a protest because protests are supposed to be peaceful as per the constitution," she told AFP. She blamed "unaccountable factions for being behind such acts", without elaborating.

On October 1, Kurdish authorities accused Hashed militants of firing rockets at the airport in Arbil, the capital city of Iraqi Kurdistan, where US troops are based. Around 90 rocket attacks have targeted the US presence in Iraq since the January drone strike, with several claimed by pro-Iran factions.