Supporters of Shia cleric Moqtada al-Sadr broke through barricades of the protected Green Zone in Baghdad after lawmakers again failed to convene for a vote.
A state of emergency has been declared in Baghdad, but not a curfew.
Security forces near the US embassy later fired tear gas to stop more protesters entering the Green Zone.
Moqtada al-Sadr wants PM Haider al-Abadi to commit to a plan to replace ministers with non-partisan technocrats.
Powerful parties in parliament have refused to approve the change for several weeks.
Earlier this week, hundreds of thousands of people marched towards the Green Zone, the most secure part of Baghdad that houses embassies and government buildings, to protest against the political deadlock.
A new protest outside the zone escalated after parliament again failed to reach a quorum on April 30.
Groups marched on the district soon after the end of a televised appearance by Moqtada al-Sadr, although he did not call for the storming of parliament.
The protesters tried to topped lawmakers attempting to flee the building.
They are reported to have begun ransacking parliament buildings. UN and embassy staff were on lockdown inside their compounds, Reuters reported.
Iraq’s system of sharing government jobs has long been criticized for promoting unqualified candidates and encouraging corruption.
PM Haider al-Abadi, who came to power in 2014, has promised to stamp out corruption and ease sectarian tensions, but he has failed to far to introduce a new technocratic cabinet.
A survey by the Pew Research Centre in 2011 found that 51% of Iraqi Muslims identified themselves as Shia, compared with 42% Sunni.
Elsewhere in Baghdad, a car bomb targeted a group of Shia Muslim pilgrims on April 30, killing at least 21 people.
The Shia cleric and his militia group, the Mehdi Army, gained prominence after the US-led invasion of Iraq in 2003. galvanizing anti-US sentiment.
Moqtada al-Sadr’s followers clashed repeatedly with US forces, whose withdrawal the cleric consistently demanded.
An arrest warrant was issued for Moqtada Sadr in 2004 in connection with the murder of a rival cleric.
Moqtada al-Sadr’s militia was also blamed for the torture and killing of thousands of Sunnis in the sectarian carnage of 2006 and 2007.
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