Baghdad's Green Zone, home to government buildings and embassies, returned to normality after 30 people were killed and 570 wounded in clashes pitting supporters of powerful Shiite cleric Moqtada Sadr against pro-Iran factions.

Since elections in October 2021, political deadlock has left Iraq without a new government, prime minister or president, due to disagreement over forming a coalition.

The tensions escalated sharply on Monday when Sadr loyalists stormed the government palace following their leader's announcement that he was quitting politics.

But Sadr's supporters trickled out of the Green Zone in a steady stream on Tuesday afternoon when he appealed for them to withdraw within the hour.

A nationwide curfew was lifted, before shops reopened and infamous traffic jams returned to Baghdad's streets on Wednesday as the government announced the resumption of school exams postponed by the unrest.

But the hurdles obstructing a solution to Iraq's political crisis remained firmly in place, with rival powers disagreeing over a path forwards.

Early elections, less than a year after the last polls, and the dissolution of parliament have been key demands of Sadr.

Sadr's rivals in the pro-Iran Coordination Framework want a new head of government to be appointed before any new elections are held.

- Snap polls -

On Wednesday, a senior aide of Sadr, Saleh Mohammad al-Iraqi, lashed out at the Framework in a strongly worded statement that pointed to a widening schism.

"Iran should reign in its Iraqi camels, or else there will be little room left for regret," he said Wednesday, referring to the Framework.

Under the constitution, parliament can only be dissolved by a majority vote, which can take place at the request of a third of lawmakers, or by the prime minster in agreement with the president.

President Barham Saleh said late Tuesday that snap elections could provide "an exit from the stifling crisis".

The Framework called for the swift formation of a new government, "to prevent a recurrence of the strife" that paralysed Baghdad this week. It also called for state institutions to resume functioning.

Prime Minister Mustafa al-Kadhemi, meanwhile, threatened to resign unless the paralysis ends.

In a call with Kadhemi on Wednesday, US President Joe Biden and the Iraqi premier "welcomed the return of security to the streets, and called on all Iraqi leaders to engage in a national dialogue," according to a White House statement.

Iraq's speaker of parliament Mohammed Halbusi on Wednesday declared three days of mourning for those killed in the clashes and Iraq's National Security Adviser Qassem al- Araji convened a security meeting to look into the circumstances behind the unrest.

Iraq's borders with Iran reopened, a day after a closing, according to Iranian media.

Iran's foreign ministry said that dialogue was the "only solution out of the current crisis."

- 'More protests' -

"Unless a proper solution is reached, more protests and violence are possible," said Iraqi political analyst Sajad Jiyad.

Falah Al-Barzanji, a 63-year-old activist, said he believed the calm would be short-lived.

"Today life has returned to normal, but the fire is still burning under the ashes," he told AFP.

"The Iraqi parliament must be dissolved and a reformist government must be installed."

Pope Francis, who visited Iraq last year, said he was "following with concern the violent events that have taken place in Baghdad" and urged dialogue.

Sadr -- a longtime player on the war-torn country's political scene, though he himself has never directly been in government -- announced he was quitting politics two days after he said "all parties" including his own should give up government positions to help overcome the deadlock.

Sadr's bloc emerged from the October election as the biggest in the legislature, with 73 seats, but short of a majority.

Since then Iraq has been paralysed due to disagreement between Shiite factions over forming a coalition.

In June, Sadr's lawmakers quit in a bid to break the logjam, which led to the Coordination Framework becoming the largest bloc.

Sadr's supporters had for weeks staged a sit-in outside Iraq's parliament, after storming the legislature's interior on July 30, demanding fresh elections be held.