The Abdel-Aziz al-Samarrai mosque was hit by U.S. aircraft that launched a Hellfire missile at its minaret and dropped a 500-pound bomb on a wall surrounding the compound.
The U.S. military said insurgents were using the mosque for a military fire base. U.S. officials said no civilians died and American commanders gave conflicting reports of insurgent casualties.
Iraqi hospital officials say at least three dozen Iraqis have been killed, among them, civilians, reports CBS News Correspondent Kimberly Dozier.
An Associated Press reporter who went to the mosque said the minaret was standing, but damaged, apparently by shrapnel. The bomb blew away part of a wall, opening an entry for the Marine assault. The reporter saw at least three cars leaving, each with a number of dead and wounded.
The heavy fighting against the Sunni insurgency coincided again Wednesday with attacks on coalition forces in southern Iraq led by militiamen loyal to anti-American cleric . For the first time Wednesday, Shiite militiamen battled Americans in the central city of Baqouba.
Since Sunday, 35 Americans, two other coalition soldiers and more than 230 Iraqis have been killed in fighting. The Iraqi figure did not include those killed at the mosque. Since the war began, at least 630 U.S. service members have died.
In major developments:
Marine Corps spokesman 1st Lt. Eric Knapp said the American force besieging Fallujah has killed more than 30 suspected insurgents and captured 51 since Tuesday night. Fifteen Marines were reported killed in fighting in Fallujah and neighboring Ramadi since Monday.
The Army said a soldier died Wednesday in the capital. Another had died Tuesday in Balad, the Sunni Triangle city north of Baghdad, the U.S. Central Command in Tampa, Fla. said.
Defense Secretary Donald H. Rumsfeld, at a Pentagon news conference with Joint Chiefs of Staff Chairman Gen. Richard Myers, discounted the strength of the al-Sadr force, which appears to have been bolstered by disgruntled, unemployed young men.
U.S. officials estimate the al-Sadr force at about 3,000 fighters.
"The number of people involved in those battles is relatively small," Rumsfeld said. "There's nothing like an army or large elements of people trying to change the situation. You have a small number of terrorists and militias coupled with some protests."
Myers said the fighting came in two broad categories. West of Baghdad in cities such as Ramadi and Fallujah, the main opposition is "former regime loyalists," including supporters of former president Saddam Hussein, and anti-American foreign fighters loyal to Abu Musab al-Zarqawi, a Jordanian-born terrorist believed linked to al Qaeda.
The Marines said they waged a six-hour battle around the Abdel-Aziz al-Samarrai mosque before calling in a Cobra helicopter which fired the missile at the base of its minaret. An F-16 dropped the laser-guided bomb, Marine Lt. Col. Brennan Byrne said.
During fighting elsewhere in Fallujah, U.S. forces seized a second place of prayer, the al-Muadidi mosque. A Marine climbed the minaret and fired on guerrilla gunmen, witnesses said. Insurgents fired back, hitting the minaret with rocket-propelled grenades and causing it to partially collapse, the AP reporter said.
Brig. Gen. Mark Kimmitt, the chief military spokesman in Iraq, said the Marines did not attack the mosque until it became clear enemy fighters were inside and using it to cover their attacks.
Rumsfeld said the United States knew risks would increase with the approach of the June 30 date for the handover of power to an interim Iraqi government.
U.S. commanders also fear violence could escalate during the religious ceremonies this weekend for al-Arbaeen, when millions of pilgrims gather in Shiite cities to mark the end of the mourning period for a 7th-century martyred Shiite saint.
The number of U.S. troops in Iraq is up, Rumsfeld said, because of the planned rotation of forces. The United States has about 135,000 troops there now.
"The United states will stay the course. We will stay until the task is complete," he said, warning that some U.S. troops ready to leave the country might have to stay a while longer.
But lawmakers are increasingly voicing concerns that more forces are needed to secure Iraq before the deadline.
"The answer is I think we need more troops. I think that the military thinks we need more troops," Sen. Joseph Biden, D-Del., told the CBS News Early Show.
Al-Sadr, meanwhile, said Iraq would become "another Vietnam" for the United States.
"I call upon the American people to stand beside their brethren, the Iraqi people, who are suffering an injustice by your rulers and the occupying army...," he said in a statement issued from his office in the southern city of Najaf. "Otherwise, Iraq will be another Vietnam for America and the occupiers."
Al-Sadr's al-Mahdi Army launched heavy gunbattles with coalition forces in the streets of at least six cities Wednesday and, for the first time, in the north.