Iraqi lawmakers have failed to vote on whether they will oust or keep the incumbent parliament speaker, prolonging the country's simmering political crisis.

Shiite lawmaker, Hassan Salim, says after the session started on Tuesday, disagreement erupted about who should run it, which in turn prompted major political blocs to walk out.

He says the next session will be held on Thursday.

Since last week, dozens of lawmakers have staged a sit-in inside the parliament, demanding the country's top political leadership — Parliament Speaker, Prime Minister and the President — step down following a Cabinet reshuffle vote delay.

Influential Shiite cleric Muqtada al-Sadr has warned lawmakers to vote on a new government or "the people will decide." Hundreds of his followers have rallied in Baghdad to press the legislators to vote.