In Baghdad, a car bomb near a hotel wounded at least five Iraqis, the U.S. military said. The target of the blast, about 100 meters from the Australian Embassy, was not immediately clear.
After the fighting in Najaf eased, people gathered at the Imam Ali shrine to look at the damage. The inner gate of the shrine, leading into the tomb of Imam Ali Ibn Abu Talib, appeared to have been hit by a projectile. Debris was scattered on the ground.
Al-Jazeera television showed a torn veil covering the gate, and damage on the wall around it. It also showed several injured people lying on the floor of the mosque compound, and an angry crowd of more than 100 shouting and shaking their fists at the site.
Supporters of Shiite militia leader Muqtada al-Sadr accused the Americans firing mortars at the mosque, and said 12 people were injured in the mosque compound. The U.S. command in Baghdad said it was investigating reports of damage.
Another projectile landed outside the shrine, about 10 meters away from the outer wall. Three militiamen were injured in that attack, and three fighters were killed in fighting in the city, al-Sadr's office said.
Imam Ali was the Prophet Muhammad's cousin and son-in-law and he is the most revered saint among Shiite Muslims.
In other developments:
1. Hand over authority to a sovereign Iraqi government.
2. Help establish stability and security.
3. Rebuild Iraq's infrastructure.
4. Draw other countries into military and other operations.
5. Move toward national elections by January.
Mr. Bush offered no exit strategy for bringing 138,000 American soldiers home, pledging instead to send more, if necessary.
While not elaborating, the president of the Iraqi Governing Council said Tuesday that the proposal for post-occupation Iraq falls short of expectations.
Fighting in Najaf and other Shiite shrine cities south of Baghdad have raised alarm among Shiite Muslims throughout the world who fear damage to the sacred sites.
U.S. officials say they have been careful to avoid damaging the shrines and have accused al-Sadr of using holy places to store weapons and seek sanctuary.
Al-Sadr launched his uprising in early April after the U.S.-led occupation authority cracked down on him, closing his newspaper, arresting a key aide and announcing a warrant against the young cleric in the April 2003 murder of a moderate religious leader.
The latest violence come after President Bush said in a nationally televised speech Monday night that the United States would stay in Iraq until it was democratic and a long-awaited U.S.-British blueprint for a post-occupation Iraqi government was present to the U.N. Security Council.
The fighting in Najaf was some of the fiercest since battles erupted there last month.
Explosions and gunfire were heard around the city's Revolution of 1920 Square and the cemetery, a warren of paths and tombs that offers numerous hiding places for rebels armed with assault rifles and rocket-propelled grenades.
Eight people were killed and 18 injured in Najaf in overnight fighting and during the day Tuesday, said Seyed Kifah Shemal, an official at Hakim General Hospital. Two people died and 14 were injured in overnight fighting in Kufa, said Riyadh Kadhem, a nurse at the Forat al-Awsat hospital in Kufa. They said the casualties were mostly civilians.
There were no reports of U.S. casualties.
In Baghdad, Iraqi police said they believed the car bomb attack may have targeted the Australian Embassy, and that the car detonated prematurely. The Australian government said its troops in Iraq were investigating, and that it was too early to tell if the embassy was the target.
Australia sent 2,000 troops to take part in the invasion of Iraq and still has 850 military personnel in and around the country.
The attack in the Jadiriyah district occurred about 50 meters from the Karma Hotel, where foreign journalists and U.N. weapons inspectors used to stay before the war that ousted Saddam Hussein.
U.S. Army Col. Mike Murray said he did not believe there were Westerners staying at the hotel. He said the car that exploded was a blue Volkswagen.
"There was a car bomb. We don't know if it was a suicide bomber or not," Murray said. "We are still trying to confirm if anybody was in the car or not."
Murray said five Iraqis were injured, including a 10-year-old boy who was critically hurt. Debris was scattered over a wide area, and windows in some buildings were shattered.