The political arm of the pro-Iran Hashed al-Shaabi paramilitary network saw its share of legislative seats decline substantially in October's election, which the group's supporters have denounced as "fraud."

Demonstrators from groups loyal to the Hashed threw projectiles and "blocked... access to the Green Zone" on three sides, before they were pushed back by police who fired in the air, a security source said, requesting anonymity.

The Green Zone is a high security area housing the US embassy and Iraq's election commission.

The Conquest (Fatah) Alliance, the political arm of the multi-party Hashed, won around 15 of 329 seats contested in the October 10 vote, according to preliminary results.

In the last parliament it held 48, making it the second-largest bloc.

The big winner this time, with more than 70 seats according to the initial count, was the movement of Moqtada Sadr, a Shiite Muslim preacher who campaigned as a nationalist and critic of Iran.

"The protesters support Assaib Ahl al-Haq and the Hezbollah brigades," the security source added.

Both these groups operate under the Hashed umbrella.

The Hezbollah Brigades dubbed last month's election as the "worst" since 2003, when dictator Saddam Hussein was toppled in a US-led invasion.

Hundreds of pro-Hashed supporters also rallied against the results on October 19.

"No to fraud, no to America," they chanted at that protest.

The Hashed demands the withdrawal of US forces from the country.

US troops remain in Iraq as part of the coalition that helped Baghdad in the fight against the Islamic State group, which the government declared defeated in late 2017.

But the Hashed, known in English as the Popular Mobilisation Forces, were themselves central in turning the military tide against IS, after Iraq's army crumbled against the jihadists' advance in 2014.

The Hashed were integrated into state security forces and the political arm rode a wave of popularity to perform strongly in the 2018 national election.

An unprecedented protest movement broke out two years ago and railed against the political class running the oil-rich but poverty-stricken country where youth unemployment is soaring.

National elections were brought forward as a concession to those protesters, who had also complained that Iraq was beholden to Iran.

Factions of the Hashed have faced accusations of targeting activists.