Shiite fighters battled Spanish troops in Najaf, drove Ukrainian soldiers from one town and seized another. Up north, violence erupted in Hawijah, and suspected Sunni gunman attacked Marines in Ramadi on Tuesday, killing a dozen.
Two more Marines were killed in Fallujah Tuesday and Wednesday, bringing the U.S. death toll in Iraq to at least 628.
A U.S. general vowed to "destroy" the forces of radical cleric, and urged him to surrender. Al-Sadr urged Iraqis to rise up against the U.S. occupation and vowed to die rather than be captured.
An Associated Press reporter in Fallujah saw cars ferrying the bodies from the mosque compound, which witnesses said had been hit by three missiles. There was no immediate confirmation of casualties, but witnesses said as many as 40 people were killed.
Until the mosque compound attack, reports had at least 30 Americans and more than 150 Iraqis dead in fighting for the neighboring cities of Fallujah and Ramadi.
In major developments:
Mr. Bush was also talking Wednesday to British Prime Minister Tony Blair, who is due in Washington for a visit next week, which it now appears will be a crisis session, reports CBS News White House Correspondent Bill Plante.
Bremer conceded that not all was going smoothly as the coalition approached a June 30 handover of sovereignty to the Iraqis, but said Iraq remains "on track" toward democracy. 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," Delaware Sen. Joseph Biden, the ranking Democrat on the Senate Foreign Relations Committee, told the CBS News Early Show. "I think we better get our act together."
Iraq's Shiite majority has largely avoided anti-U.S. violence, shunning al-Sadr's virulent anti-U.S. rhetoric as well as the insurgency led by Sunnis in central Iraq. U.S. officials have expressed concern that al-Sadr could start cooperating with the Sunni guerrillas.
The U.S.-led coalition announced an arrest warrant for murder against al-Sadr on Monday and suggested it would move to capture him soon, after a series of weekend uprisings in Baghdad and cities and towns to the south that took a heavy toll in both American and Iraqi lives.
Clashes continued overnight between militiamen from al-Sadr's al-Mahdi Army and coalition troops in Kut, Karbala and the mainly Shiite neighborhood of Sadr City in Baghdad. At least 12 Iraqis were killed in Kut and four in Baghdad, along with two Iranians caught in the crossfire in Karbala, according to doctors.
The Ukrainian Defense Ministry said its troops were forced to evacuate Kut early Wednesday after al-Sadr forces hit the position with mortar fire throughout the night.
Militiamen battled Spanish soldiers in Najaf, south of Baghdad. An Iraqi taxi driver was killed in the crossfire, a hospital official said.
Bulgaria asked the U.S. to send troops to reinforce its battalion of 450 soldiers in the southern city of Karbala, reports CBS News' Lisa Barron.
Gunmen attacked a police car Tuesday night in Youssifiya, south of Baghdad, killing two policemen.
The al-Mahdi Army, which may number 10,000 fighters, appeared to be in control of Kut and Kufa, occupying government buildings and roaming the streets, as Iraqi police stood aside. Witnesses reported that a British civilian working for a private security company was killed when militiamen took over the company's office in Kut.
In Fallujah, Marines and gunmen were engaged in heavy battles in the Dubat neighborhood on the eastern side of the city and in other part in the center of the city, witnesses said. U.S. warplanes opened fire on groups of Iraqis in the street.
Rocket-propelled grenade fire set a U.S. Humvee ablaze, injuring soldiers inside, witnesses said.
Hundreds of U.S. Marines and Iraqi police have surrounded Fallujah, a stronghold of the anti-U.S. insurgency west of Baghdad, since Monday.
Rumsfeld said Marines did not intend to attack the town, but were hunting people identified as having mutilated the corpses of four American contractors last week. However, the U.S. brought in heavy firepower because of stiff resistance.
The militants still move freely in the town center, daring the Americans to approach them, reports CBS News Correspondent Kimberly Dozier. The Marines are moving forward block by block.
"It is the most difficult, the most dangerous, the most time-consuming battles we could possibly fight," said CBS News military analyst Mitch Mitchell, a retired Army colonel. "When we get into cities, that's the worst of all possible situations. It takes away most of our advantages."
U.S. warplanes firing rockets destroyed four houses in Fallujah after
nightfall Tuesday, witnesses said. Among the dead were 26 people — including 16 children and up to eight women, said Hatem Samir, head of the clinic at Fallujah Hospital. Others were killed in street battles before dawn and into the day Wednesday.
In nearby Ramadi on Tuesday, gunmen in a cemetery opened fire on U.S. patrols. A Marine commander confirmed that 12 Marines died in two battles that raged over three hours, one of them across a mile-long front. The commander also said his troops had captured fighters from Syria. Witnesses said at least two Iraqis died.