Heavy fighting has been raging in Basra as thousands of Iraqi troops battle Shia militias in the southern city.
At least 30 people have died in the operation, which is being overseen in Basra by Iraqi PM Nouri Maliki, a day after he vowed to "re-impose law".
Oil-rich Basra is in the grip of a bitter turf war between armed groups, including the Mehdi Army, analysts say.
Clashes have spread to other parts of Iraq, including Baghdad's Sadr City,
where the Mehdi Army fought rival Shia.
The Mehdi Army - which supports radical Shia cleric Moqtada Sadr - has threatened a nationwide campaign of civil disobedience.
The powerful militia declared a truce last August which had been credited with helping restore stability to parts of Iraq.
The BBC's Adam Brookes says three Iraqi army brigades were deployed from Baghdad to Basra as back-up for the offensive, and that up to 15,000 troops could be involved.
Some of the fiercest fighting in the operation - dubbed Saulat al-Fursan (Charge of the Knights) - has focused on Mehdi Army strongholds.
British military spokesman Maj Tom Holloway told the BBC no UK troops were involved on the ground but its forces have carried out air surveillance to support Iraqi army tanks and artillery.
The UK military returned control of Basra to the Iraqis in December and concentrated its forces at the city airport.
The Iraqi commander in charge, Lt Gen Ali Ghaidan, said the operation aimed to purge Basra of what he called "outlaws".
Moqtada Sadr has threatened "general civil disobedience"
He said his forces had confiscated weapons and roadside bombs during raids across Iraq's second city.
Routes into Basra have been sealed off, according to reports.
One resident of the city told the BBC: "The streets are very dangerous, there's continuous exchange of fire in areas very close to my house, even though my neighbourhood is relatively safer than others."
The BBC's Paul Wood says the fighting in Basra can be seen as the government trying to impose law and order but also as part of the power struggle within the Shia community.
He says such intra-Shia violence could be just as dangerous to hopes of peace as sectarian hatreds or the insurgency.
The offensive comes a day after the authorities in Basra imposed an indefinite night-time curfew.
Police have now also imposed curfews in the cities of Kut, Samawa, Nasiriyah, Hilla and Diwaniyah.
Moqtada Sadr called for "general civil disobedience in Baghdad and the Iraqi provinces" if the attacks did not end.
In Sadr City, Mehdi Army fighters reportedly ordered Iraqi police and soldiers out of the district and there have been clashes between rival militias.
Hundreds of protesters marched in the Iraqi capital, calling on shops to shut.
The Mehdi Army also took control of several areas in Kut, 175km (110 miles) south-east of Baghdad.
Moqtada Sadr last month renewed the group's ceasefire, under which it pledged not to attack rival armed groups or American forces in Iraq.
But the truce is said to have come under strain in recent weeks as US and Iraqi forces detained militia members.
Iraqi Foreign Minister Hoshyar Zebari told the BBC: "Militias have taken over almost the city and law and order has collapsed, although it is not a hopeless case because the government is taking measures to reverse the situation.
"Remember, Basra is the lifeline of Iraq. Most of Iraq's oil exports go through Basra."