Embattled Iraqi parliament speaker Salim al-Juburi Tuesday announced the suspension of parliament sessions "until further notice" after a week of turmoil during which lawmakers brawled and sought to sack him.

The political crisis comes as Iraq battles the Islamic State jihadist group, which overran large areas in 2014, and contends with a serious economic crisis caused by low oil prices and years of mismanagement and corruption.

Both the United States and the United Nations have warned that the crisis could distract from efforts to combat IS.

Some MPs voted last week to remove Juburi and elected Adnan al-Janabi as his interim replacement, meaning there are now two claimants to the speakership.

Juburi insists the vote to sack him and his deputies was invalid because the session lacked the necessary quorum, but his opponents are seeking to move ahead with selecting replacements.

"I announce the suspension of sessions... of the Iraqi parliament until further notice," Juburi said in a statement.

But Janabi has called for a session to be held on Thursday, so MPs may still meet without Juburi's leadership.

Juburi's decision was taken to "preserve the reputation of parliament" and prevent it from being "a place for conflict", he said.

There has been plenty of conflict in parliament over the past week: lawmakers held an overnight sit-in and threw punches in the chamber, as well as seeking to sack Juburi.

The turmoil began with disagreement over proposed cabinet line-ups presented by Prime Minister Haider al-Abadi, but shifted to calls for Juburi to go.

Abadi has sought to replace the cabinet of party-affiliated ministers with a government of technocrats, but has faced significant opposition from powerful political parties that rely on control of ministries for patronage and funds.

President Fuad Masum proposed a plan to end the parliamentary leadership crisis, but the session he called for failed to resolve differences among lawmakers.

Under Masum's plan, a copy of which was obtained by AFP, parliament was to convene for an "extraordinary session" to vote on whether or not to remove Juburi and his two deputies.

The proposal was accepted by Juburi but rejected by his opponents on the grounds that it would return to the issue of whether or not he should stay in office, which they insist has already been resolved.

According to a parliamentary official who was present, Janabi presided at the Tuesday session, announcing that nominations would be accepted to replace Juburi and his deputies and saying the next meeting would be on Thursday.

The move was criticised by lawmakers who do not support Juburi's removal, meaning parliament will remain divided for now.

Abadi called on Monday for parliament to put aside its differences and do its job, saying he hoped for a vote on a new cabinet within days -- something that looks increasingly unlikely.