Anti-government rallies have rocked Baghdad and the Shiite-majority south since October 1, with demonstrators calling for a complete overhaul of a regime they deem corrupt, inefficient and overly beholden to Tehran.

"The revolution continues!" shouted one demonstrator at a protest encampment in central Diwaniyah.

Protesters blocked off public buildings one by one in the southern Iraqi city and put up banners reading, "The country is under construction -- please excuse the disruption".

Sunday marks the latest deadline -- already pushed back twice by President Barham Saleh -- for parliament to choose a new premier to replace Adel Abdel Mahdi, who quit last month.

Parliament speaker Mohammed al-Halbussi on Sunday travelled to Arbil, capital of the Kurdish autonomous region in northern Iraq, to discuss who could become the next premier, the presidency there said.

Officials say Iran wants to install Qusay al-Suhail, who served as higher education minister in the government of Abdel Mahdi.

"This is exactly what we oppose -- Iranian control over our country," said 24-year-old student Houeida, speaking to AFP in Baghdad's Tahrir Square, the epicentre of the protests.

The demonstrators categorically reject Suhail's candidacy, along with anyone from the wider political establishment that has been in place since dictator Saddam Hussein was deposed in 2003.

"Hundreds of martyrs have fallen and they are still not listening to our claims", said 21-year-old student Mouataz, in Tahrir Square.

"We want a prime minister with integrity, but they bring back a corrupt man in their image whom they will allow to continue robbing us," he added.

- 'Iraq must be Iraqi again' -

In a bid to secure the necessary parliamentary majority for a new premier, Shiite powerhouse Iran enlisted the services of a Lebanese Hezbollah official to negotiate with Sunni and Kurdish parties.

The post of prime minister is by convention held by a Shiite in Iraq's post-2003 political system.

In a Twitter plea to Saleh, one opposition Sunni lawmaker called Sunday for the president to "violate the constitution rather than plunge the country into bloody chaos by choosing a figure people have already rejected".

Some in parliament -- the most fragmented in Iraq's history -- argue that Saleh should use Article 81 of the Constitution, which authorises the president to step in as prime minister himself if there is no agreement among lawmakers on a candidate.

As the midnight deadline loomed, Saleh received a letter from the Supreme Court, which he had turned to for guidance, saying that "all options are open", further adding to the confusion.

If the post remains vacant at midnight, the constitution will place Saleh himself in the role of acting premier for just 15 days until political leaders can agree on designating a new prime minister.

In a sign of the protesters' unprecedented influence, top Shiite cleric Grand Ayatollah Ali Sistani, who is said to have made and unmade every premier in the post-Saddam era, has been notably absent from the manoeuvrings this time around.

The protest movement has been hit by intimidation, including assassinations perpetrated by militias, according to the UN.

Around 460 people have been killed since October 1, and some 25,000 have been wounded.

Yet the protesters appeared to regain some confidence on Sunday.

Overnight, demonstrators in Diwaniyah and Basra, another southern city, had declared a "general strike".

They burnt tyres to block roads linking southern cities to Baghdad, an AFP correspondent said.

The road to Umm Qasr port -- vital for imports -- near Basra was among those blocked.

In Karbala and Najaf, two Shiite holy cities, striking students closed schools and gathered in their thousands, AFP correspondents said.

In Nasiriyah, protesters blocked bridges and several roads while all public buildings remained closed.

Protesters are demanding the fall of Saleh and Halbussi, accusing them of procrastinating.

"Iraq must become Iraqi again, and if the president does not help us, we will force him out too," asserted student Houeida, buoyed by the renewed momentum in Tahrir Square.