Residents said the streets of Basra were deserted on Thursday and that shops and businesses were shut.
Iraq's third largest city, located 550km south of Baghdad, is home to about 1.5 million people.
Colonel Karim al-Zaidi, a police spokesman, said the convoy of Major-General Abdul Jalil Khalaf, the city's police chief, was hit by a suicide car bomber around 1am on Thursday [2200 GMT Wednesday] as it passed through the streets of the city.
Al-Zaidi said three policemen were killed in the attack but Khalaf was unharmed.
A fire raged near Basra after a bomb exploded underneath an oil pipeline, Iraqi officials said.
Behind the scenes, government officials and senior Mahdi Army figures loyal to Muqtada al-Sadr, the Shia leader, are said to be holding peace talks.
The meetings were held in Najaf on Thursday to try to end the crisis, Liqa Ali Yassin, a member of al-Sadr's 32-member parliamentary bloc, said.
And in a public appeal, according to his office, al-Sadr has called for a "peaceful and political solution" to end the fighting.
An al-Sadr official in Najaf said that the statement was being distributed to all the offices of the group across Iraq.
In a bid to contain the clashes, Iraqi authorities have imposed a three-day total curfew in Baghdad.
Security officials said on Thursday the curfew will be effective until 5am local time (0200 GMT) on Sunday.
A US government employee was killed in Thursday's Green Zone mortar attacks and three more employees were wounded, according to Mirembe Nantongo, a US embassy spokeswoman.
Jazeera's James Bays, reporting from Baghdad, said the crackdown in Basra was meant as a show of strength by al-Maliki.
"I think the prime minister is trying to put his stamp in this operation. No one expected that he would go to Basra," he said.
"Al-Maliki wants to show that he is in control because in the past, he was seen as a weak, impotent leader."
The latest clashes in Basra came in defiance of a Friday deadline given by al-Maliki for armed groups to give up their weapons or face "severe penalties".
The violence began on Tuesday, when Iraqi government forces launched operations to rid Basra of what officials called "lawless gangs".
|Supporters of al-Sadr marched through|
Baghdad on Thursday [GALLO/GETTY]
Fighting then spread to al-Sadr's stronghold in Baghdad and other cities.
Al-Sadr demanded on Thursday that al-Maliki leave Basra and send a parliamentary delegation for talks on resolving the crisis.
He also threatened to launch a civil revolt if the attacks against the fighters were not halted.
Before the current unrest, Basra had become the battlefield for a turf war between the Mahdi Army and two rival Shia factions - the Supreme Iraqi Islamic Council (SIIC) of Abdel Aziz al-Hakim and the smaller Fadhila party.
The three factions are fighting to control the huge oil revenues generated in the province, which was transferred to Iraqi control by the British military in December.
The military operation in Basra has touched off protests and gun battles by al-Sadr's supporters elsewhere in the country.
In the Iraqi capital, they staged marches on Thursday condemning the crackdown.
In the Sadr City district, demonstrators shouted: "Maliki you are a coward! Maliki is an American agent! Leave the government, Maliki! How can you strike Basra?"
Protests were also held in the southern city of Amara.
The Basra operation has extended north to Kut, where six Iraqi security personnel and six civilians have reportedly been killed as troops fought militia members street by street.
To the west in Diwaniya, Shia fighters attacked a police station, killing two people.
In Tikrit, at least seven civilians were reportedly killed and nine others were wounded in US air strikes that destroyed two homes, according to Al Jazeera sources.
Khalaf Haloul, a resident of Amara, told Al Jazeera by telephone that clashes between Iraqi forces and the Mahdi Army were under way there as well.
He said mortars and rockets could be heard across the city.
Mahdi Army fighters had deployed in all areas of Amara in anticipation of military attacks, Haloul said.
Also on Thursday, Iraqi sources told Al Jazeera that about 60 civilians were killed in a US air strike on the city of southern city of Hilla, although there were conflicting reports.
Iraqi security sources said that 29 people were killed.