BAGHDAD -- In direct confrontation with the American-backed government in Iraq, thousands of supporters of the powerful Shiite cleric Moktada al-Sadr and his Mahdi Army militia took to the streets of Baghdad on Thursday to protest the Iraqi Army's assault on the southern port city of Basra, as intense fighting continued there for a third day.

In Basra, there seemed to be no breakthrough in the fighting by either side. As much as half of the city remained under militia control, hospitals in some parts of the city were reported full, and the violence continued to spread. Clashes were reported all over the city and in locations 12 miles south of Basra.

The Iraqi Army's offensive in Basra is an important political test for the government of Prime Minister Nuri Kamal al-Maliki and for American strategy in Iraq. President Bush sought to portray the fighting in a positive light on Thursday, declaring the offensive by Mr. Maliki's government a "bold decision."

But if the army's assault in Basra leads the Mahdi Army to break completely with its current cease-fire, which has helped to tamp down attacks in Iraq during the past year, there is a risk of escalating violence and of replaying 2004. That year, the militia fought intense battles with American forces that destabilized the entire country.