The clashes are mainly between Iraqi government security forces and members of the Imam Al-Mahdi Army militia, loyal to radical Shi'ite cleric Muqtada al-Sadr.
The seriousness of the situation is shown by the reported presence in Al-Basrah of Iraqi Prime Minister Nuri al-Maliki.
Iraqi security forces are making what appears to be a large-scale drive to oust the Al-Mahdi Army and other radical Shi'ite groups from the city.
Police spokesman Major Karim al-Zubaidi said ground forces started their assault before dawn, and fighting was reported in six areas of the city where the Shi'ite militias are strong.
The police say at least four people have been killed, and local hospitals are said to be filling up with wounded.
It's not clear why the government has chosen to launch its offensive now. The Sadrists recently renewed a unilateral six-month cease-fire, which they declared last August.
But security in Al-Basrah has been declining for months, with growing tension and clashes between the Al-Mahdi Army and other Shi'ite factions, as well as with criminal gangs seeking control of sections of the city.
A British military spokesman said British troops encamped near Al-Basrah airport are taking no part in the fighting. The British withdrew to that camp in December, when they handed over security matters in Al-Basrah to Iraqi forces.
British spokesman Major Tom Holloway said Iraqi Prime Minister al-Maliki is in Al-Basrah to personally oversee the operation. After touring the city on March 24, al-Maliki spoke of a "brutal campaign" by gunmen against the population of the city. He said their efforts at destabilization are going hand-in-hand with oil, arms, and drugs smuggling, and that the government intends to stamp this out.
Spokesmen for al-Sadr and the Al-Mahdi Army have reacted with outrage to al-Maliki's moves, saying the Al-Mahdi Army is being especially targeted. Harith al-Athari in Al-Basrah expressed regret at the fighting, and said the Sadrists are ready for negotiations to calm things.
In Baghdad today, pro-Sadr demonstrators took to the streets to show their support for their leader.
AP quoted unnamed U.S. officials as saying there is no quarrel with Sadrists who are observing the truce, but that they want to strike at renegade Shi'ite elements which they believe are linked to Iran.
The subject of Iranian interference in Iraq has also been raised by the senior U.S. military commander in Iraq, General David Petraeus. He said on March 24 that he has evidence that Iran was behind the bombardment of the Green Zone in Baghdad a day earlier.
Petraeus told the BBC that he believed Iran has trained, equipped, and funded insurgents who fired the barrage of mortars and rockets at the Green Zone, the center of Iraqi government and U.S. activities. He offered no evidence to support his allegations.