Thousands of people protested for reforms on Monday at the Iraqi capital's heavily fortified Green Zone, where the government is headquartered, for the second time in less than a month.

The call to rally at the Green Zone, where the US and British embassies are also located, went out over a loudspeaker at a sit-in at Baghdad's Tahrir Square, an AFP journalist said.

The demonstrators set out running from the sit-in site, crossed Jumhuriyah Bridge and gathered at the Green Zone entrance near parliament.

Powerful Shiite cleric Moqtada al-Sadr organised a two-week sit-in at the Green Zone in March, calling for a technocratic government and threatening to have his supporters storm the area.

A senior Sadr Movement official told AFP that the demonstrators would not try to enter the Green Zone on Monday.

"It is a message we want to deliver to the government and the parliament," Ibrahim al-Jaberi, the head of Sadr's east Baghdad office said, apparently referring to the fact that demonstrators could be quickly mobilised and gathered at the Green Zone.

"We will withdraw to Tahrir Square this evening," he said.

Sadr, the scion of a powerful clerical family, called off the March sit-in after Prime Minister Haider al-Abadi presented a list of cabinet nominees to parliament.

But efforts to replace the current party-affiliated ministers have faced serious opposition from powerful parties that rely on control of ministries for patronage and funds.

Iraqi political blocs presented their own nominees and most of Abadi's candidates were replaced on a second list.

Cabinet reform efforts were then overshadowed by days of chaos in parliament, including an overnight sit-in, a brawl between lawmakers and an attempt to sack the speaker.

Demonstrators began the sit-in at Tahrir Square on Saturday, after a parliamentary session aimed at selecting replacements for speaker Salim al-Juburi and his deputies failed to reach a quorum.