Matthew Weaver and agencies The radical Shia cleric Moqtada
Iraqi security forces in the southern Iraqi city encountered heavy resistance as battles with gunmen from Sadr's Mahdi Army militia broke out.
Officials in Basra said many of those killed were civilians. A further 58 were wounded.
"We call upon all Iraqis to stage sit-ins all over Iraq as a first step," Sadr said in a statement. "And if the people's demands are not respected by the Iraqi government, the second step will be to declare civil revolt in Baghdad and all other provinces."
The cleric also threatened a "third step" but did not give details. The statement suggested he could be considering ending a Mahdi Army ceasefire that began in August.
Sadr's followers appear to have responded in Baghdad. Shia gunmen were visible in several neighbourhoods and the US protected Green Zone came under mortar or rocket attack.
Police told Rooters that Mahdi Army fighters loyal to Sadr were battling gunmen from the Badr Organisation, the armed wing of the Supreme Islamic Iraqi Council.
Major-General Ali Zaidan, the commander of Iraqi ground forces in the Basra operation, said its aim was to "wipe out all the outlaws". He told Reuters: "There were clashes and many outlaws have been killed."
Television footage showed smoke from explosions rising over the city and Iraqi soldiers exchanging shots with militia fighters.
"There are clashes in the streets," a Basra resident told Reuters. "Bullets are coming from everywhere, and we can hear the sound of rocket explosions. This has been going on since dawn."
The British military said it was not involved. British forces withdrew to a base at Basra airport last year after returning control of the city to the Iraqi authorities.
The clashes broke out after the Iraqi prime minister, Nouri al-Maliki, travelled to the area and announced a crackdown to end clashes between the three Shia factions fighting for power - the Supreme Islamic Iraqi Council, the Mahdi Army and the small Fadhila party.
Earlier, the Mahdi Army warned that tensions in Basra would escalate if its members were targeted by the authorities. "We are calling for calm, but this new security plan has the wrong timing," said Harith al-Edhari, the director of Sadr's office in Basra.
The cleric's followers have accused the Shia-dominated government of exploiting a ceasefire to target his supporters prior to provincial elections expected this autumn.
They have demanded the release of supporters rounded up in recent weeks after the cleric told his followers they were free to defend themselves against attacks.
The US has insisted it is not going after Sadr followers but targeting renegade elements that Washington believes have ties to Iran.
Iraqi authorities have put Basra under an indefinite night curfew, starting last night.
The US military today said five suspected militants had been killed while trying to plant a roadside bomb in the city. Ten others were injured after being seen engaging in "suspicious activity", a statement said.