The Sadr militia is itself fractured.
"Attacking the Sadr militia was not an option anybody wanted," one senior Pentagon official said.
General Kimmitt said the order had gone out "to destroy the Sadr militia - deliberately, precisely and powerfully."
Some 500 armed Sadr militia burn tires, forming roadblocks and promising jihad near the office.
Hashim Ibrahim Hassan, a politician from the northern Griot neighborhood, said the Sadr militia had recently taken over a Shiite mosque, or husseiniya, that his father built in 1954.
Throughout the clashes, American military spokesmen have stressed the point that fighting with the Sadr militia has been undertaken under the political authority of the new government.
So the plan focused on chipping away at the Sadr militia with controlled strikes, and working behind the scenes with more moderate Shiite clerics to isolate him and undercut his local support.
An official of the Sadr militia disputed that figure.
They have tried to draw out the Sadr militia and have threatened to destroy it if it does not disband.
Qasim Fakhir, who said he was a member of the Sadr militia, said the Shiites must confront the Americans in Najaf.