In Baghdad, another soldier from the 220th Military Police Brigade was killed and two were wounded when a roadside bomb exploded Friday morning. No further details were released.
The deaths bring to 101 the number of U.S. soldiers killed in combat since President Bush declared an end to major combat operations May 1.
The Americans involved in the firefight at a senior Shiite cleric's headquarters were members of the 101st Airborne Division, said Maj. Mike Escudie of U.S. Central Command in Tampa, Florida.
Gunfire broke out again Friday morning in the same area Karbala, where Thursday night's encounter may have signaled a new determination by the Americans to disarm religious-based militias and enforce curfews. Sporadic clashes continued for about 12 hours after the initial battle.
In other developments:
In Karbala, an armored personnel carrier of the U.S.-led coalition opened fire Friday morning as screaming men, women and children fled for cover. Shiite gunmen defiantly shouted, "Allahu Akbar!" — "God is great!" The gunfire soon ended, but young Shiites still manned rooftop and street positions with assault rifles and rocket-propelled grenades.
The gunmen abandoned their positions hours later, but several Polish jeeps and armored cars remained stationed less than 200 yards away from the cleric's house. At least two Polish snipers could be seen at nearby rooftops. Normal traffic also resumed in the area as life went on normally elsewhere in Karbala, with thousands of pilgrims, many Iranians, congregating at the city's two holy Shiite shrines.
The Central Command said Thursday night's engagement "involved an exchange of small arms fire and rocket-propelled grenades as Iraqi authorities and Coalition military police were investigating reports of armed men congregating on a road near the (Imam Abbas) mosque after curfew."
Malik Kazim, a gunman who said he took part, said the fighting involved a coalition patrol of armored vehicles and Humvees that passed at about 11:45 p.m. by the offices of a local senior Shiite Muslim cleric, Mahmoud al-Hassani, which were guarded by at least 20 gunmen.
Karbala, where the Polish military has local command, has been under a 9 p.m. curfew since Tuesday, and the international patrol ordered the gunmen inside the offices, they refused and a gunbattle ensued, Kazim said.
The Americans opened fire on the armed guards "without any provocation or warning," said Abu Ali, an aide to al-Hassani. He said al-Hassani, who moved to Karbala from Baghdad following the fall of Saddam Hussein's regime in April, has moved to a secret location with his family Friday morning.
The Central Command said two members of the Iraqi security forces also were killed and five wounded, and Abu Ali said eight of the guards were killed.
Kazim said intense gunfire lasted about a half-hour.
Large pools of blood could be seen on the street Friday morning, along with dozens of bullet holes in the walls, some large-caliber.
Al-Hassani is a lesser-known grand ayatollah — the highest clerical rank in Shiism. Rivalries among Shiite factions have led to sporadic violence in recent weeks, as the sect, suppressed under Saddam's regime, flexes its new political muscle as a majority in Iraq.
Thursday night's clash in Karbala appeared to reflect a determination by the U.S.-led coalition to minimize any challenge to its authority from armed religious militants.
"There are laws governing carrying of weapons in Iraq, and coalition forces will do what they need to do to enforce the law," spokesman Lt. Col. George Krivo said last week.
Such a policy is likely to lead to further confrontations with Shiite groups, which generally endorsed or accepted the U.S. attack on Saddam's regime, but which recently have built up militias as they vie with each other for primacy in the Shiite community.
Iraq's foreign minister has a warning for a young Shiite Muslim cleric, Muqtada al-Sadr — that his private militia will be disarmed by force if necessary. Al-Sadr's fighters have fought recent gunfights with U.S. forces and other Shiite factions in Iraq.
In Baghdad's Sadr City district, a stronghold for the firebrand Shiite cleric, about 6,000 Shiites chanted "No No U.S.A., Yes Yes Muqtada" at Friday prayers. Less than a half-mile away, U.S. tanks, armored personnel carriers and dozens of soldiers blocked off streets leading to a building housing the Sadr City council.