Protesters in Baghdad's Green Zone have left the heavily fortified government district after a 24-hour sit-in but pledged to return by the end of the week if their demands for political reform are not met.

The dispersal came on a day two suicide car-bomb attacks in southern Iraq killed at least 32 people and injured 75 others.

Sunday's blasts, claimed by the Islamic State of Iraq and the Levant (ISIL, also known as ISIS) group, occurred in the centre of the southern city of Samawa.

Iraq has endured months of discontent prompted by Haider al-Abadi's attempt to replace party-affiliated ministers with technocrats as part of an anti-corruption drive.

A divided parliament has failed to approve the prime minister's proposal amid scuffles and protests.

Abadi's arrest order

Deep frustration over the deadlock culminated in a breach on Saturday of the Green Zone by supporters of Muqtada al-Sadr, the powerful Shia leader.

Protesters stormed the parliament, clashed with police and broke the barricades.

Abadi called for their arrest on Sunday.

Iraq's political crisis deepens with storming of parliament by Sadr loyalists

Abadi's statement ordered "the interior minister to track down the perpetrators who assaulted the security forces, the citizens and members of the council of representatives and were involved in vandalising public property and to present them to court so they can have a fair trial and face justice".

Sadr and his supporters want the political system put in place following the US-led invasion in 2003 to be altered.

As it stands, entrenched political blocs representing the country's Shias, Sunnis and Kurds rely on patronage, resulting in widespread corruption and poor public services.

The major blocs have until now blocked Abadi's reform efforts.

"In Iraq, a change is demanded by almost most Iraqis, especially by those out of power," Ghassan al-Atiyyah, head of Iraqi National Initiative, told Al Jazeera.

"Ultimately, the ball is in our court. We have to devise a way to improve the situation. Failure of the secular and ethnic parties in moving Iraq forward has created an atmosphere for change."

Abadi has given warning that continued turmoil could hamper the war against ISIL, which controls large parts of northern and western Iraq and has frequently targeted the seat of power.

The Green Zone protesters issued an escalating set of demands, including a parliamentary vote on a technocrat government, the resignation of the president, prime minister and parliamentary speaker and new elections.

If none of the demands are met, a spokesperson for the protesters said in a televised speech, they would resort to "all legitimate means", including civil disobedience.

The peaceful defusing of the crisis came after Abadi convened a meeting with Iraq's president, parliament speaker and political bloc leaders who called the breach "a dangerous infringement of the state's prestige and a blatant constitutional violation that must be prosecuted".

OPINION: Sadr's challenge to Iraq's sectarian politics

The Green Zone, a 10sq km district on the banks of the Tigris River which also houses many foreign embassies, has been off-limits to most Iraqis since the US-led invasion in 2003.

In an unprecedented breach on Sunday, hundreds of people pulled down and stormed over concrete blast walls, celebrating inside parliament and attacking several deputies.