On Thursday the heavily-fortified Green Zone in the heart of the Iraqi capital again came under rocket and mortar fire.
More than 130 Iraqis are reported to have died in three days of heavy fighting, with hundreds more injured.
One American was killed in Thursday's attacks on the Green Zone – the second to die this week.
On Friday the Iraqi parliament is due to hold an emergency session to discuss ways to end the violence.
Nouri al-Maliki, the Iraqi prime minister, has based himself in Basra to personally oversee military operations in the city and has said there will be "no retreat" against the Shia militias.
The city saw a third straight day of fighting on Thursday despite al-Maliki's deadline for fighters to surrender by Friday or face "severe penalties".
Few journalists have been able to travel to the city, but reports say Basra's streets were deserted with shops and businesses shut.
"We have made up our minds to enter this battle, and we will continue until the end," the prime minister said in a speech broadcast on state TV.
He said Iraq had become a "nation of gangs, militias and outlaws" and he was undertaking an "historic mission" in Basra to restore "the law of the land".
The crackdown in Basra is seen as a key test for al-Maliki, with the ability of Iraq's leaders and armed forces to control such situations central to US hopes of pulling its own forces out of the country.
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.
|Thousands of protesters marched through |
Baghdad's Sadr City in support of al-Sadr [AFP]
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.
Al Jazeera correspondent James Bays, reporting from Baghdad, said the Iraqi leader wanted to be seen putting his stamp on the operation.
"Al-Maliki wants to show that he is in control," he said, "because in the past, he was seen as a weak, impotent leader."
At a speech in Ohio on Thursday George Bush, the US president, praised al-Maliki for launching a "tough battle against militia fighters and criminals" in Basra, citing it as evidence that Baghdad is increasingly able to handle security without US leadership.
Bush's speech at the of the US Air Force museum in Dayton is one of a series of addresses made in defence of the five-year-old war in Iraq, and intended to prove that the so-called troop "surge" is having an effect.
"Some members of Congress decided the best way to encourage progress in Baghdad was to criticize and threaten Iraq's leaders while they're trying to work out their differences," he said.
"But hectoring was not what the Iraqi leaders needed," Bush said, adding that what the Iraqis needed was security "and that is what the surge has provided."
|The crackdown is seen as a key test for |
al-Maliki and the Iraqi military [AFP]
Rejecting suggestions that Iraq's leaders were "foot dragging", he said they were "striving to build a modern democracy on the rubble of three decades of tyranny."
Praising what he said was al-Maliki's "bold decision" to take on the Basra militias, he said the move was a turning point in showing that Iraq is taking on more responsibility.
"There's a strong commitment by the central government of Iraq to say that no one is above the law," Bush said.
Critics in the US congress however say Bush is painting a far too rosy picture of the situation in Iraq.
"The president asserts that real progress has been made in Iraq. But if that were truly the case, our troops would be coming home soon," said Harry Reid, the Democrat majority leader in the US senate.
On Thursday thousands of al-Sadr's supporters joined protest marches in Baghdad, calling on the Iraqi prime minister to resign.
In the neighbourhood of Kazimiyah, protesters denounced al-Maliki as a "new dictator" as they carried a coffin bearing a crossed-out picture of the US-backed prime minister.
Protests also took place in the mainly Shia district of Sadr City.
Al-Sadr himself released a statement on Thursday calling for a political solution to the growing crisis and an end to the "shedding of Iraqi blood."
But the statement, released by a close aide, stopped short of ordering the Mahdi Army to halt fighting.