Baghdad, Iraq ? U.S. forces fought heavy battles Tuesday in Najaf and Fallujah but appeared no closer to regaining control of the cities after a 3-week-old uprising in each.

Outside Najaf, American troops fought one of their biggest battles so far against the militia of hard-line Shiite Muslim cleric Muqtada al-Sadr. It erupted as U.S. troops moved into the area to replace Spanish units that have withdrawn from Iraq, and it raised fears of a potentially explosive escalation of violence at what is seen widely as the most politically sensitive locale in Iraq.

In Fallujah, tanks and an American AC-130 gunship poured cannon fire into the city in a brief, intense nighttime assault that reportedly targeted the poor northern neighborhood of Jolan. The area is a stronghold of Sunni Muslim guerrillas who ignored a U.S. deadline for handing over their weapons under the terms of a truce negotiated by the city’s political leaders.

Aljazeera, the Arab television network, showed explosions and burning buildings in Fallujah, where tens of thousands of residents have fled this month’s fighting. There was no word of casualties.

U.S. military spokesmen said that in Najaf 64 members of al-Sadr’s militia, the Mahdi Army, were killed. They did not immediately report any U.S. casualties, and no estimate was available for the numbers of civilians killed.

Al-Sadr’s militia seized control of much of Najaf and the adjacent city of Kufa, as well as other locales, early this month after the U.S. occupation authority announced it would arrest him for allegedly having ordered the murder of a rival cleric last year. U.S. troops expelled the militia from other areas but have avoided moving against al-Sadr’s home in Kufa or his office, which is adjacent to Najaf’s Imam Ali Mosque, the most important religious shrine for Iraq’s 15 million Shiites.

The U.S. occupation authorities in Iraq are struggling to find a way to put down al-Sadr’s uprising, and the one in Fallujah, without damage to shrines or civilian losses that could ignite broader warfare. Accusing U.S. forces of “a provocation,” Qais Al-Khazaali, a Mahdi’s Army spokesman, said on Aljazeera that “the red line still has not been crossed.”

An Iraqi man searches through the rubble of his house in Fallujah, Iraq, after it was shelled by a mortar during a fight between Iraqi Sunni insurgents and U.S troops. The fighting took place Monday; the resident returned home Tuesday.

In both cities, the United States has tried to avoid military action by negotiating with local authorities. But there is little sign that city elders in Fallujah or Shiite leaders in Najaf can enforce any compromises on the militants who now hold much of those cities.

Hospitals in Najaf reported receiving between 23 and 37 dead by nightfall Tuesday, according to varied accounts from news agencies. It was unclear how many were among the 64 guerrillas killed cited by U.S. officials, or how many might have been civilians.

The only reported U.S. combat death Tuesday came in Baghdad, where a soldier was shot while guarding a bus station. With that, the U.S. death toll for April rose to 115, equaling the number of military personnel killed during the initial invasion of Iraq in March and April of last year.