In Basra, Major Abdul Jalil Khalaf, the police chief, said fighting was taking place in three quarters of the city between the security forces and members of the so-called Soldiers of Heaven sect.
Police said that one policeman was killed during clashes, in the al-Andalus neighbourhood in central Basra.
Police also said men attacked the police headquarters in the al-Tamimiya neighbourhood as clashes spread to a number of districts in the city's centre.
Witnesses said aircraft belonging to the US-led force flew over Basra and Iraqi tanks took positions on the streets, some 550km south of Baghdad.
An indefinite curfew was immediately placed on the city by Iraqi authorities.
The clashes in Nasiriya, about 350km south of the capital, were in the east of the city, a police official said.
It is not yet known how many members of the Shia sect have been killed, but police said the head of the sect in Basra had been killed in the fighting.
The fighting comes as Shias across Iraq have marked Ashura, one of the holiest days in Shia Islam, when they commemorate the killing of Imam Hussein by armies of Yazid in 680.
|Bodies of Shia fighters lay|
in the streets in Basra [AFP]
Basra's police chief said the fighting by the Shia sect in Basra was being led by Ahmed al-Hassani Al-Yamani.
Yamani claims to be an ambassador of Imam Mahdi, an eighth century imam who vanished as a boy and whom Shias believe will return to bring justice to the world.
During Ashura in 2007, the "Soldiers of Heaven" clashed with US and Iraqi forces outside the holy cities of Najaf and Karbala.
Last year's fighting left 263 members of the sect dead, including their leader, Dhia Abdul Zahra Kadhim al-Krimawi, also known as Abu Kamar.
Hundreds of thousands of people crowded the streets of Karbala for the ceremonies on Friday, which reach their peak on Saturday.
The shrine city, around 110km south of Baghdad, was under a tight security cordon, with around 20,000 security force members deployed.
Ashura ceremonies have been targeted by Sunni groups in the past and on Thursday eight people were killed when a suicide bomber blew himself up during a procession outside a mosque in Baquba, 60km north of Baghdad.
British forces handed over control of the oil-rich province of Basra to Iraqi forces in mid-December, amid warnings that it could descend into violent turf wars between Shia groups.
The UK expects to sharply reduce its nearly 5,000-strong troop presence in the province.
But around half that number will stay at their base at Basra airport to support the Iraqi security forces and for training purposes.