The fighting in Najaf between US forces and the Shia militia of Moqtada Sadr has been going on now for over a week and looks to be intensifying.
By Jonathan Marcus
BBC diplomatic correspondent
It is still not clear if US troops, along with Iraqi government forces, have embarked upon an all-out assault to destroy Mr Sadr's militia once and for all.
Damage to the shrine could have an impact far outside Najaf
The radical cleric is seen by both the interim Iraqi government and the Americans as posing a major challenge to the political process in the country.
Many other Shia leaders are also suspicious of his ambitions.
But there is great unease about the location of the fighting - so close to the Imam Ali shrine, one of Shia Islam's most important sites - and urban warfare always risks major civilian loss of life.
In practical terms the US military has gathered a large force of marines, backed up by army units and air power.
Iraqi government troops are also involved, though their participation may be largely for political reasons - not least to signal that this is an operation that has the full backing of Iraq's interim Prime Minister Iyad Allawi.
The battlefield - especially the vast cemetery - is a frightful jumble of gravestones and passageways - ideal terrain for snipers and ambushes.
Nonetheless the well-trained US marines should have the advantage provided they are set clear objectives.
Dangers of defeat
But the stakes could not be higher.
If this goes wrong - supposing there were major damage to the mosque or massive civilian casualties - the credibility of not just the Americans but of the Iraqi prime minister himself would be on the line.
Mr Sadr's men have shown themselves to be determined and effective fighters.
What is not clear is how far he will be able to use the US assault to enrage Iraq's Shia majority and spread the fighting to other towns.
There has already been violence in the southern city of Kut. And the last thing the government or the Americans want is a widespread Shia revolt.