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Supporters of Iraq's powerful cleric started to withdraw from Baghdad's Green Zone on Tuesday after he urged them to end a protest following violence that killed 23 of them.

Sadr gave followers "60 minutes" to withdraw from the high-security Green Zone, after which he would threatened to "disavow" those who remained.

"I apologise to the Iraqi people, the only ones affected by the events," Sadr told reporters from his base in the central Iraqi city of Najaf.

Moments after Sadr's speech, broadcast live on television, his supporters were seen beginning to leave the Green Zone, and minutes after that, the army lifted a nation-wide curfew imposed since violence erupted on Monday.

Tensions have soared in Iraq amid a political crisis that has left the country without a new government, prime minister or president for months.

They escalated sharply after Sadr's supporters on Monday afternoon stormed the government palace inside the Green Zone following their leader's announcement that he was quitting politics.

Sadr, a grey-bearded preacher with millions of devoted followers who once led a militia against American and Iraqi government forces after the 2003 US-led overthrow of dictator Saddam Hussein, announced Monday his "definitive retirement" and said he had "decided not to meddle in political affairs".

Overnight Monday and on Tuesday morning, clashes raged between Sadr's supporters and the army and men of the Hashed al-Shaabi, former Tehran-backed paramilitaries integrated into the Iraqi forces.

On Tuesday morning, medics updated the toll of Sadr supporters killed to 23, with some 380 others injured -- some with bullet wounds and others suffering tear gas inhalation.

A mass funeral was held Tuesday in the Shiite holy city of Najaf for some of the protesters killed in Baghdad.