Nouri Al-Maliki said fighters from al-Sadr's Mahdi Army had 72 hours to give themselves up or would face "severe penalties".
"Those who were deceived into carry weapons must deliver themselves and make a written pledge to promise they will not repeat such action within 72 hours," he said.
Al-Maliki was speaking at an army base in Basra from where he is overseeing military operations in the city.
More than 50 people have died in the last two days of heavy fighting and the Iraqi government has sent reinforcements to Basra to back up soldiers moving street by street through the most volatile parts of the city.
Elsewhere in the country at least 11 Iraqis were reported killed in a raid by a US helicopter in the central city of Hilla.
US military officials, who have been providing back-up to the Iraqi military, said they believed four Shia fighters had been killed in the raid.
Major-General Kevin Bergner, a US military spokesman said Iraqi police called for US air support after clashing with a number of "special group criminals" in Hilla, about 120km south of the capital, Baghdad.
But he added US forces were not participating in the clashes beyond playing a "liaison" role.
Another military spokesman said: "Initial reports indicate that four special group criminals were killed in the air strike."
The US uses the term "special groups" when referring to al-Sadr's Mahdi Army militia.
The latest fighting broke out in Sadr City, a large poor area in the capital, early on Wednesday.
The violence comes after Iraq's security forces launched raids on strongholds of Mahdi Army fighters on Tuesday.
|The Iraqi PM has given Mahdi Army fighters in |
Basra 72 hours to surrender [AFP]
As the fighting broke out, al-Sadr issued a statement calling for demonstrations across the country and threatened "civil disobedience" if attacks by US and Iraqi forces on members of his movement continued.
"We demand that religious and political leaders intervene to stop the attacks on poor people," a statement read by Hazam al-Aaraji, an al-Sadr representative, said.
"We call on all Iraqis to launch protests across all the provinces. If the government does not respect these demands, the second step will be general civil disobedience in Baghdad and the Iraqi provinces."
Al Jazeera's James Bays, reporting from Baghdad, said that a spokesman for al-Maliki was reporting that some fighters had surrendered following the prime minister's ultimatum.
But he added there were reports that heavy fighting was continuing in parts of Basra.
"I think the prime minister is trying to put his stamp in this operation. No one expected that he would go to Basra," our correspondent said.
"Al-Maliki wants to show that he is in control, because in the past, he was seen as a weak, impotent leader."
The US claims that members of the so-called "special groups" are trained in Iran in the use of sophisticated weaponry, including rockets and lethal roadside bombs known as "explosively formed penetrators" that can cut through US armoured vehicles.
|Al-Sadr has called for 'civil disobedience'|
Amid the accusations, the military says that Iran could contribute to ending the violence in Iraq, calling on Tehran to use its influence to assist in improving security in Basra.
Bergner said: "There is no question that the government of Iran has significant influence in Basra, in the province and in southeastern Iraq in general.
"We would love to see the government of Iran fulfil its commitments to help improve security and stability [in Basra] ... and reduce the activities of those operating outside the law."
Bergner also said the operation was aimed at improving security in the Basra province ahead of provincial elections in October.
"The prime minister's assessment is that without this operation there will not be any hopeful prospect of improving security in Basra," Bergner said.
Falah Shenshal, a member of parliament allied to al-Sadr, told Al Jazeera that al-Maliki was targeting political opponents.
"They say they target outlaw gangs, but why do they start with the areas where the sons of the Sadr movement are located?"
"This is a political battle ... for the political interests of one party [al-Maliki's Dawa party] because the local elections are coming soon.
"They are using the law for their political interests. We will ask the parliament to drop confidence from the Maliki government."
The Mahdi Army has grown frustrated with a ceasefire imposed by al-Sadr last year.
Its fighters say the ceasefire has been abused by US and Iraqi forces to make indiscriminate arrests ahead of provincial elections.
The US military says it is targeting only "rogue" members who have broken the ceasefire, and has cited the truce as a main factor in a significant drop in violence across the country.