Mohammad Allawi announced his own nomination as premier on Saturday, which marked exactly four months since the anti-government movement erupted and two months since outgoing prime minister Adel Abdel Mahdi resigned under growing pressure.

Demonstrators had demanded a politically independent successor who had not served in government and for them, ex-communications minister Allawi did not make the cut.

"Mohammad Allawi is rejected, by order of the people!" read a new sign hung in the holy city of Najaf on Sunday.

Young men with their faces wrapped in checkered scarves had spent the night torching car tyres in anger at Allawi's nomination, an AFP reporter in the city said.

Main highways leading out of Najaf and streets within the city were still blocked off with smouldering tyres on Sunday morning.

Kut, about 170 kilometres (100 miles) southeast of Baghdad, saw hundreds hit the streets chanting, "If it's been tried before, it shouldn't be tried again!"

In Diwaniyah, further south, protesters marched into government buildings to demand they close for the day, while students began sit-ins at schools and universities.

Protesters in Hillah blocked off all roads leading into the city and chanted, "Allawi is not the people's choice!"

Allawi, named as a consensus candidate after months of political paralysis, now has a month to pull together his cabinet, which will be subject to a vote by parliament.

In his first formal address, he pledged to form a representative government, hold early parliamentary elections and ensure justice for protest-related violence -- all key demands of demonstrators.

More than 480 people have died and nearly 30,000 have been wounded since the rallies began on October 1, but few have been held accountable for the bloodshed.

The protests first demanded an end to corruption, better services and jobs for unemployed youth, but they quickly spiralled to calls for a total government overhaul.