Iraqi premier Haider al-Abadi called Monday for the fractious parliament to put aside its differences and do its job, saying he hopes a new cabinet will be approved in days.

Iraq has been hit by weeks of political turmoil surrounding Abadi's move to replace the current cabinet of party-affiliated ministers with a government of technocrats.

His efforts to change the cabinet, which have faced significant opposition from powerful political parties that rely on control of ministries for patronage and funds, were overshadowed by chaos in parliament last week.

Both the United States and the United Nations have warned that the political crisis could distract from efforts to combat the Islamic State (IS) jihadist group, which overran large areas of Iraq in 2014.

"I call on parliament to convene immediately to overcome the obstacles and contribute to developing solutions to the challenges facing the country," Abadi said in a statement.

"I look forward to parliament being able to undertake its... legislative and supervisory role and voting on the cabinet reshuffle in the coming days," he said.

Abadi presented a list of cabinet nominees at the end of March, but the political blocs put forward their own candidates, and most of the premier's original list was replaced on a second presented to MPs last week.

Some MPs demanded the opportunity to vote on Abadi's original list -- from which at least two candidates had already withdrawn -- but the session was adjourned on Tuesday without a vote.

Dozens of lawmakers then began a sit-in and spent the night in parliament, while an "emergency" session on Wednesday ended with MPs shouting, shoving and throwing punches in the chamber.

And on Thursday, lawmakers voted to sack parliament speaker Salim al-Juburi and his deputies, but the speaker insists the session at which the vote was held lacked a quorum and was therefore invalid.

Juburi opponents tried to meet on Saturday to select replacements for him and his deputies, but MPs from the Shiite Badr bloc said they would not attend, leaving it without a quorum.

Demonstrators then began a sit-in in central Baghdad for the second time in the past month, leading to increased security measures and major traffic jams.

The political turmoil comes as Iraqi forces battle to regain more ground from IS, which has lost significant territory but still holds a major chunk of western Iraq.

An operation against IS west of Baghdad was apparently delayed in March after security forces were withdrawn to provide security for demonstrators in the capital.