BAGHDAD - U.S. Secretary of State Condoleezza Rice arrived in Baghdad on Sunday for an unannounced visit one day after the Shiite cleric Muqtada al-Sadr threatened an all-out war against the Iraqi government.

Rice called al-Sadr a coward hiding in Iran while praising Iraqi Prime Minister Nouri al-Maliki for his recent offensive in the southern port city of Basrah that sparked an uprising by al-Sadr's militia, the Mahdi Army.

Since the March 25 government offensive in Basrah, where the Mahdi Army dominates, the Sadrists and their militia have angrily accused the government of trying to undercut their movement prior to October provincial elections, when they will likely win many of the Shiite southern provinces from their Shiite rivals in the government.

If al-Sadr's militia, conservatively estimated at about 60,000 men, were to rise up, it could mean the end of the drop in violence in Iraq and an inter-sectarian war. Already, thousands of government soldiers have deserted in both Basrah and Sadr City, refusing to fight the Shiite militia. Some deserted because of threats to their families, others from a moral objection by the mostly Shiite Iraqi security forces to fighting their Shiite brothers.

Iraqi government officials have told McClatchy Newspapers that al-Maliki, who gained wide support from Sunni officials for taking on the Mahdi Army, went into the fight with no preparation and now is in a battle that he can't extract himself from. U.S. support for al-Maliki puts U.S. forces on one side of a bloody intra-Shiite showdown.

Rice used her visit to praise al-Maliki's choice to take on the militia. Fighting al-Sadr, who has declared that resistance against U.S. forces is legitimate, is an "internal Iraqi matter," she said.

"But, clearly, the prime minister has laid down some ground rules which any functioning democratic state would insist upon, having to do with, you know, arms belonging to the state, not to -- not in private hands," she said. "The current circumstances come out of what I think is a very important and indeed appropriate action that the Iraqi government has taken."

Al-Sadr has consistently called for peace since he froze his militia Aug. 29 and again in February; his freeze has been a major factor in curbing violence in Iraq. But Sadrists say their movement has come under attack continually since that time, and they feel humiliated because they have been asked to stand down.

The Iraqi government seemed to ignore al-Sadr's "final warning" Saturday of a "war until liberation" if the U.S.-backed Iraqi security forces didn't stop attacking his followers. Iraqi soldiers continued their confiscation of weapons and the evacuation of government buildings in Basrah.