Three people were injured in the twin explosions, a police official told AFP on condition of anonymity.

The attack is the first time a political party has been targeted in the Iraqi capital since the electoral campaign started in mid-April.

"Two bombs were thrown at the ICP headquarters," in Al-Andalus Square, spokesman Jassem al-Hilfi told AFP.

He accused the "corrupt who cannot accept that they lost" the parliamentary elections of being behind the attack.

The bombings are "a threatening message aimed at frightening us to stop us from pursuing the path of reform and change," he added.

The Iraqi Communist Party receives threats "all the time", Hilfi said.

Sadr's Marching Towards Reform anti-corruption campaign saw the alliance win 54 seats in the May 12 vote, to become the biggest bloc in Iraq's 329-seat parliament.

The pro-Iranian Conquest Alliance, made up of ex-fighters from mainly Shiite paramilitary units that battled the Islamic State group, came second in the elections.

The Victory Alliance of Prime Minister Haider al-Abadi, who declared victory over IS in December, performed worse than expected and came third.