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.

Iraq's complex political landscape means weeks of horse-trading are likely before a new government takes shape.

The May 12 vote, the first since Iraq declared victory over the Islamic State group, was marked by record abstention levels as many voters stayed away in a rebuke to the perceived corruption of the ruling class.

IS, which seized swathes of Iraq during a lightning 2014 offensive, has lost nearly all the territory it once held but the group is still capable of carrying out sporadic attacks.

Five people were killed on Friday when an IS suicide bomber detonated his explosive belt in a park in northern Baghdad, where families had gathered for the suhur meal taken before daybreak during the holy Muslim month of Ramadan.