Shia Muslims came to the shrine when they heard about the clashes
One of Iraq's holiest Shia Islamic shrines has reportedly been damaged in clashes between US troops and the forces of militant cleric Moqtada Sadr.
Correspondents say the incident in Najaf - in which at least three people were injured - is likely to spark outrage among Iraq's Shia majority.
The news followed overnight fighting in Najaf and Kufa in which at least five civilians were killed and 19 wounded.
Al-Jazeera TV showed damage to the inner gate of the shrine leading to the tomb and debris strewn on the ground.
It also showed that a veil covering the entrance to the tomb had been torn and injured people lying on the floor of the compound.
It was not clear who fired the missiles.
A representative of militant cleric, Ahmed Shebani, said five or six missiles had hit the building.
There was no immediate comment from the US military, or reports of US casualties.
Imam Ali was the Prophet Mohammed's cousin and son-in-law and he is the most revered saint among Shia Muslims.
The gilded dome of the shrine was damaged earlier this month.
The US says it is careful to avoid damaging holy shrines and says Mr Sadr's militia has been using them to store weapons and ammunition.
In the past few days the US military has stepped up the pressure on the radical cleric in an offensive it is calling Operation Iron Sabre.
Dozens of Mr Sadr's men have been killed but both sides, it seems, are determined to fight on.