Hundreds took to the streets of the capital and cities across the south on Tuesday in the first major challenge to the government, formed a year ago this month.

Security forces fired tear gas and live rounds to disperse the crowds, leaving one dead and 200 wounded in Baghdad and another protester dead in the south, health officials said.

The violence 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.

And 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".

The demonstrators in Tahrir Square in the heart of Baghdad voiced a range of grievances -- state corruption, failing public services, unemployment and even the sidelining of a popular Iraqi general last week.

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

By early evening, it had degenerated into violence, with riot police using tear gas and water cannons and then opening fire with live and rubber bullets to disperse the crowds.

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

On Wednesday morning, Tahrir Square remained sealed off by a heavy police presence.

Parliament has ordered an investigation into the violence. Its human rights committee has already criticised security forces for their "suppression" of the demonstrations.

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

And in his first comments on the demonstrations, Prime Minister Adel Abdel Mahdi paid tribute to the security forces, blaming the violence on "aggressors who... deliberately created casualties".

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