The protests are the first significant popular challenge to Prime Minister Adel Abdel Mahdi, who formed his government a year ago this month and who controversially blamed the violence on "aggressors" among the protesters.

On Wednesday, the iconic Tahrir Square in Baghdad where hundreds of protesters had gathered the previous day was sealed off by security forces, with some demonstrators gathering around the edges.

Smaller crowds took to the streets in Al-Shaab in north Baghdad and Zaafaraniya in the south, an AFP correspondent reported, with riot police attempting to disperse them with tear gas and live rounds fired in the air.

Like the previous day, protesters railed against state corruption, failing public services and unemployment.

"I came out today in support of my brothers in Tahrir Square," said Abdallah Walid, 27.

He spoke to AFP in Zaafaraniya, where protesters were burning tyres on streets lined with riot police vehicles.

"We want jobs and better public services. We've been demanding them for years and the government has never responded," he said.

In Al-Shaab, unemployed graduate Mohammad Jubury said protesters "feel like foreigners in our own country."

"No state would attack its own people like this. We're being peaceful, but they fired," he told AFP.

- Calls for restraint -

Medical sources said about a dozen people were admitted to hospitals across Baghdad on Wednesday, most of them suffering from tear gas inhalation.

Riot police had also used water cannons, rubber bullets and live rounds to break up the protest of around 1,000 people in Tahrir Square on Tuesday.

Heavy gunfire was heard into the night around Tahrir Square. It was not clear if bullets were fired directly at protesters or into the air.

Tuesday's clashes left one dead and 200 wounded in Baghdad, and another protester dead in the south, health officials said.

Volleys of gunfire sounded through the night from the Sadr City district where the funeral was held for the protester killed in Baghdad.

The day's bloodshed drew condemnation from President Barham Saleh, who urged "restraint and the respect for the law".

"Peaceful protest is a constitutional right granted to citizens," he said late Tuesday.

The UN's top official in Iraq, Jeanine Hennis-Plasschaert, expressed "grave concern" on Wednesday, saying she "deeply regrets the casualties".

She urged authorities to "exercise restraint in their handling of the protests".

- 'Without poster or party slogan' -

Unusually for Iraq, no political faction had explicitly called for Tuesday's protest, which appeared to be largely spontaneous.

The liberal newspaper Al-Bayina Al-Jadida said the protests were, "for the first time without flag, without poster or party slogan."

They come after months of simmering frustration with Abdel Mahdi over a perceived lack of progress on corruption, unemployment or services.

Routine power cuts leave consumers without main electricity for up to 20 hours a day and, according to the World Bank, youth unemployment runs at around 25 percent, or double the adult rate.

Protests over the same issues engulfed the southern city of Basra last summer and effectively ended Abdel Mahdi's predecessor Haider al-Abadi's chances of a second term.

Abdel Mahdi now faces a similar challenge.

Late Tuesday, he paid tribute to the security forces and blamed the violence on "aggressors who... deliberately created casualties".

Interior ministry spokesman Saad Maan told state media on Tuesday that "infiltrators were behind the violent acts in the protests today."

Their statements drew widespread online criticism, as some other politicians had thrown their weight behind the protesters.

Nationalist cleric Moqtada al-Sadr called for a "fair investigation" into the events in Tahrir Square.

Parliament, too, has ordered a probe into the violence and its human rights committee criticised security forces for their "suppression" of the demonstrations.