At least 60 people were injured when Iraqi troops drove back thousands of mainly Shia Muslims protesting against corruption and security failures.
Soldiers fired real and rubber bullets at the protesters, as well as tear gas.
Some reports, citing hospital sources, said four people had been killed and 90 injured in the clashes.
On Saturday two coffins draped in flags were driven through part of the city, flanked by mourners.
Iraqi President Fuad Masum called on protesters to "abide by the law and apply self-restraint".
In a statement published on the presidency website, Mr Masum said violent rallies would distract security forces from preventing terror attacks.
It was the second time this month that protesters managed to break into the city's government area.
Shia Muslim cleric Moqtada Sadr condemned the use of force by the police, and voiced support for the demonstrators' "peaceful [and] spontaneous revolt".
The protesters accuse the government of neglecting much needed reforms, as it struggles with its campaign against the so-called Islamic State group (IS) and declining oil revenues.
The Sunni jihadist group controls parts of western and northern Iraq and has been behind a wave of recent attacks that have left dozens killed.
Some demonstrators managed to break into the prime minister's office and parliament.
Baghdad's Green Zone houses the parliament, key government buildings and many foreign embassies.
The authorities later said they had completely regained control of the area and the protesters had withdrawn.
The Shia cleric and his militia group, the Mehdi Army, gained prominence after the US-led invasion of Iraq in 2003. galvanising anti-US sentiment.
Mr Sadr's followers clashed repeatedly with US forces, whose withdrawal the cleric consistently demanded.
An arrest warrant was issued for Mr Sadr in 2004 in connection with the murder of a rival cleric.
His militia was also blamed for the torture and killing of thousands of Sunnis in the sectarian carnage of 2006 and 2007. Mr Sadr fled to Iran during that period.
In 2011, Mr Sadr returned from his self-imposed exile to Iraq, taking a more conciliatory tone and calling for Iraqi unity and peace.
Prime Minister Haider al-Abadi, who came to power in 2014, has promised to stamp out corruption and ease sectarian tensions.
He has been pressing for radical reforms and wants to form a government of technocrats, but has been blocked by lawmakers, the BBC's Jim Muir in Baghdad reports.
Parliament is so deeply split that it cannot hold a meeting because no side can achieve a quorum, our correspondent adds.
Iraq's system of sharing government jobs has long been criticised for promoting unqualified candidates and encouraging corruption.
Funerals have taken place in Baghdad for two people killed when protesters stormed the city's fortified government district, the Green Zone on Friday.