By Stephen Kalin and Ahmed Rasheed

BAGHDAD (Reuters) - Protesters camped out in Baghdad's Green Zone for 24 hours left the heavily fortified government district on Sunday after issuing demands for political reform but they pledged to return by the end of the week to keep up the pressure.

Iraq has endured months of wrangling prompted by Prime Minister 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 proposal amid scuffles and protests.

Deep frustration over the deadlock culminated in a dramatic breach on Saturday of the Green Zone by supporters of powerful Shi'ite Muslim cleric Moqtada al-Sadr.

Sadr wants to see Abadi's proposed technocrat government approved, ending a quota system blamed for rampant corruption. Powerful parties have resisted, fearing the dismantling of patronage networks that sustain their wealth and influence.

Abadi has warned continued turmoil could hamper the war against Islamic State, which controls large swathes of northern and western Iraq.

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 spokeswoman for the protesters said in a televised speech that they would resort to "all legitimate means" including civil disobedience.

Hundreds of protesters peacefully exited the Green Zone moments later.

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

They said the high-level meetings would continue in coming days "to ensure radical reforms of the political process".

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A politician who attended the talks said Abadi had faced accusations of mishandling the crisis. Another said the conflict had become an intra-Shi'ite battle over who will run Iraq.

Two suicide car bombs claimed by Islamic State killed at least 32 people and wounded 75 others on Sunday in the center of the southern city of Samawa, police and medics said.

GREEN ZONE: "EVEN THE PLANTS ARE DIFFERENT"

The Green Zone, a 10-square-kilometre district on the banks of the Tigris River which also houses many foreign embassies, has been off-limits to most Iraqis since the U.S.-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.

Many protesters, including some women and children, had spent Sunday in the square, taking refuge inside event halls from 37 degree Celsius heat, while others lay on the grass or cooled off in a large fountain topped with a military statue.

A demonstrator named Humam said he was shocked by the contrast between the poverty in which most Iraqis like him live and the comparative luxury inside the central district, which he had never entered before.

"There is electricity and street lighting, there is more water here than I expected. Even the plants are different," he said. "It is the people's right to enter this area because (the politicians) are living in conditions that don't even exist in Iraq. I didn't imagine this existed in Iraq."

Another protester who referred to parliament as "the council of traitors" said he wanted to see top officials removed.

"They have done nothing good for Iraq, only destruction, sectarian wars, hunger and no services."

(Additional reporting by Thaier al-Sudani; Writing by Stephen Kalin; Editing by Raissa Kasolowsky and Gareth Jones)