Hundreds of Iraqi protesters calmly filed out of Baghdad's heavily fortified Green Zone on Sunday after they breached the area's walls and stormed parliament to demand reforms one day earlier.

Prime Minister Haider al-Abadi had ordered authorities earlier in the day to arrest protesters who attacked security forces, lawmakers and damaged property during the breach.

Rally organizers said their decision to leave the Green Zone, home to government offices and foreign embassies, "emanates from a strong position."

Their departure from the Green Zone was aimed at giving the country's decision-makers the chance to "come to their senses," the organizers said Sunday in a televised statement.

They vowed to take further action unless parliament approves a cabinet line-up of independents proposed by al-Abadi in a single session.

"If this demand is not met, we will move to the second stage, which is to unseat the three top leaders of the country," they said, referring to the posts of prime minister, parliamentary speaker and the head of the state.

"The third stage will be a call for early elections."

TV footage showed groups of the protesters, who are loyal to influential Shiite Muslim cleric, heading towards the Green Zone gates.

No arrests among protesters were reported.

On Saturday, thousands of al-Sadr's loyalists poured into the Green Zone and descended on parliament, after the legislature delayed a vote on the proposed cabinet nominees.

Hours later, the protesters left parliament, only to start a sit-in at a nearby square to push for long-delayed reforms.

On Sunday, Al-Abadi held a crisis meeting with parliamentary Speaker Salim al-Jabouri and President Fouad Massoum, with other leading politicians in attendence. Al-Sadr was not among them.

They condemned parliament's storming and attack on lawmakers, calling it a "serious aggression against the state prestige."

"The aggressors must be brought to justice because what happened constitutes a flagrant violation of the constitution," the top leaders said in the statement released by Massoum's office. 

The breach marked a dramatic twist in the political crisis in Iraq, which is struggling against Islamist insurgents.

For several months, Iraq has witnessed numerous demonstrations against corruption and inefficient public services.

In response, al-Abadi, a Shiite, proposed a package of major reforms, including the formation of a government of independent technocrats. But powerful political blocs in parliament have thwarted the move.

Al-Abadi has warned that the current crisis can hamper the country's US-backed fight against the Islamic State extremist group, which controls key areas in Iraq's Sunni heartland.

In recent months, Islamic State has carried out a series of attacks in Iraq mainly targeting the country's Shiite community and security forces.

At least 30 people were killed and 55 wounded Sunday in a bomb attack in the mostly Shiite southern town of Samawa claimed by Islamic State.

The extremist group said in a statement, circulated by its supporters online, that two suicide bombers detonated back-to-back car bombs in Samawa, around 300 kilometres south of Baghdad.

The attack was the second in two consecutive days to be claimed by Islamic State. The statement could not be independently verified.

Local officials said the attack involved a car bomb and another explosive device.

On Saturday, 24 people were killed in a car bombing targeting Shiite pilgrims in a Baghdad suburban area. 

Islamic State, a radical Sunni militia, regards Shiites as heretics.

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