Hundreds of members of Sadr's Mehdi Army mingled with demonstrators in the southern city of Basra and fired at British army and Iraqi police patrols, said a military spokesman.
The demonstrations appeared to be prompted by the offer of a 250,000-dinar (170-dollar) bounty by Sadr's representative in the city, Abdelsattar Al-Bahadili, for the capture of British soldiers.
British newspapers on Saturday printed fresh allegations that the country's soldiers systematically beat and abused Iraqi prisoners in their southern zone of control.
British troops kept a tight grip on the centre of Basra, with troops ringing the governor's office. Tensions have been high after days of fighting between Sadr supporters and the coalition in southern and central Shia cities.
Five militia members were killed and nine British soldiers were wounded when gunbattles erupted in Basra and the town of Amara further north, according to the British army and Iraqi medics.
None of the British soldiers' injuries was life threatening.
The clashes followed fighting in the holy cities of Karbala and Najaf on Friday that left 20 of Sadr's militiamen dead, as the US-led coalition attempted to isolate the firebrand cleric.
Fresh skirmishes broke out in Karbala on Saturday as US forces continued to moved against Sadr's followers, an AFP correspondent said.
In other violence, three members of the same family, two women and a man, were killed in a bomb attack against a police official's house near Baqubah, north-east of the capital. Two Polish soldiers also died, one from a roadside explosion and another in a traffic accident.
Asked whether the crisis with Sadr would end before the June 30 deadline for the handover of sovereignty, a coalition official told AFP: "You can't set a timeline on this stuff... You can't set a timeline on a military operation."
Sadr, who is wanted for the murder of a rival cleric last year, has been holed up in Najaf for more than a month but slipped past US patrols to neighbouring Kufa for prayers on Friday, trailed by hundreds of his militiamen.
In a typically fiery sermon on the Muslim holy day he demanded that President George W. Bush go on trial over the abuse of detainees in US-run jails in Iraq. Images of abuse shocked the world when they were broadcast on US television last week.
During hours of questioning by lawmakers on Friday, US Defence Secretary Donald Rumsfeld said that many more "blatantly sadistic" pictures and videos were likely to emerge of sexual humiliation and degrading treatment of prisoners at the Abu Ghraib prison, west of Baghdad.
In his weekly radio address on Saturday, Bush reiterated his condemnation of the abuse that has thrown his administration into crisis, but continued to claim that only a small number of soldiers were involved.
The International Committee of the Red Cross said it had warned the United States of such human rights abuses more than a year ago. It said the ill-treatment of prisoners was systematic and amounted to torture.
The US commander for detention facilities in Iraq vowed on Saturday to end all abusive practices but said there were no immediate plans to close the prison at the centre of the controversy. "Currently we will continue to operate at the Abu Ghraib facility," said Major General Geoffrey Miller amid calls from US politicians to shut it down.
He promised that officers would honour the Geneva Conventions that protect prisoners. "I give you my personal guarantee we will continue to do that seven days a week, 24 hours a day," he told reporters.
Meanwhile two rival sets of talks were held in Baghdad over the future of the Iraqi government after the power handover on June 30.
Some 500 eminent Iraqis from across the political spectrum met to set up a rival political force free of US influence and the US-appointed Governing Council.
The group of moderate Shias, Sunnis and Arab nationalists called for an end to the occupation, vowed to boycott political groups set up by the United States, demanded a stronger army and called for talks with UN special envoy Lakhdar Brahimi.
Sheikh Jawad al-Khalisi, a senior Shia cleric, said they wanted the handover of power to Iraqis "done under the umbrella of the United Nations and not the Coalition Provisional Authority (CPA)", the US-led authority in Iraq since Saddam Hussein's regime fell in April.
Brahimi meanwhile met members of the US-appointed Governing Council and assured them he wanted their input on the formation of an interim government to rule the country from July 1 until elections scheduled in January.