Protesters withdrew from Baghdad's Green Zone on Sunday after breaking into the fortified area and storming Iraq's parliament in an unprecedented security breach the day before.

The move, which lessens the pressure on politicians in Baghdad, came as rare bombings in the south killed 33 people and wounded dozens.

"The protest organising committee announces the withdrawal of the demonstrators from the Green Zone," it said in a statement, citing respect for a major Shiite pilgrimage as the reason for their departure.

The statement was distributed by the office of Shiite cleric Moqtada al-Sadr, whose supporters make up the vast majority of the demonstrators.

Demonstrator Hussein al-Ali said that the announcement was made at Ihtifalat Square, where protesters had gathered, and that demonstrators then departed, but would be back later.

Protesters pulled down or scaled slabs of heavy concrete blast wall on Saturday to enter the Green Zone, where Iraq's main government institutions are located, the culmination of weeks of political turmoil and inaction by parliament.

Some remained overnight, and hundreds of people combined a festive demonstration with sight-seeing in the previously off-limits area on Sunday.

Protesters waved flags, clapped and chanted slogans in front of a grandstand from which Saddam Hussein once delivered addresses, in an area bordered by giant statues of twin crossed swords held in hands said to have been modelled on Saddam's own.

The Green Zone breach allowed Iraqis access to places they have rarely if ever been able to enter before.

- Parallel world -

"This is the first time I've been here since I came with my school under Saddam," said 32-year-old Yusef al-Assadi, who took a "selfie" in front of the monument to the unknown soldier.

Assadi said it was striking "how rich this place is. Here, there is air conditioning and electricity everywhere, but the people of Iraq suffer from power cuts all the time."

Many Iraqi politicians live in luxury, while most average citizens make do with abysmal services that include only a few hours of government-provided electricity per day at the height of summer.

Prime Minister Haider al-Abadi's office said he had ordered the pursuit of people involved in attacks or vandalism, but while security forces were deployed at Ihtifalat Square on Sunday, they did not take action against the demonstrators.

Protesters attacked at least one MP as well as cars they believed belonged to lawmakers, and broke into offices in parliament.

But others sought to contain the destruction, and many were content to take photographs of themselves in parliament, with some sitting in seats usually occupied by lawmakers.

The fact that security forces may fear the repercussions of crossing Sadr will likely hamper Abadi's directive.

The protesters broke into the Green Zone after MPs again failed to approve new ministers to replace the current party-affiliated cabinet.

Both Abadi and Sadr have called for the change, but powerful political parties that rely on control of ministries for patronage and funds have opposed the move.

- South Iraq bombings -

"Even the most sectarian of Iraqis are seeing the failure of their leaders and their system," said Patrick Skinner, a former CIA case officer who is now with The Soufan Group consultancy.

"The question might not be 'why now' as it relates to the anger, but 'why it took so long'. Their system is not working," he said.

Parliament approved some of Abadi's nominees earlier in the week, but "they were replacing figures who were easy to replace", said Kirk Sowell, a Jordan-based political risk analyst who is the publisher of Inside Iraqi Politics.

"Abadi just looks more and more impotent... He is just very weak. He will not be impeached. But he is being made less relevant by the day," Sowell said.

Baghdad security forces were already on high alert prior to the storming of parliament due to the annual commemoration of Imam Musa Kadhim's death, which sees tens of thousands of Shiite faithful walk to a shrine in northern Baghdad.

But at least 23 people were killed in a bombing targeting pilgrims just outside Baghdad on Saturday.

On Sunday, two suicide attackers from the Islamic State group detonated car bombs in the city of Samawa, some 230 kilometres (145 miles) south of Baghdad.

Local security and medical officials put the death toll at 33 and said at least 50 other people were wounded.

Such attacks are rare in Iraq's deep south, which is overwhelmingly Shiite and has been largely spared the chaos that has plagued Iraq for years.