Apparently, al-Sadr's Medhi militia was fighting US forces in August 2004 to a standstill, when a mediator (Dr Mowaffaq Rubai'e – now Iraq national security adviser and "closely associated with the American authorities in Baghdad") was sent in to end the fighting. Al-Sadr signed an agreement with Rubai'e to end the fighting in exchange for respecting Najaf's holy sites.
The representative returned to Baghdad to show the agreement to Iraqi authorities. But on his return to Najaf, Rubai'e found US forces poised to make a different deal with al-Sadr. Here's how Cockburn reports it based on his interview with Rubai'e:
Muqtada al-Sadr's movement went on to stand candidates in the 2005 national assembly elections in Iraq, winning 32 seats. Those candidates joined the current government after its ascension to power, but recently withdrew support for it.
It was agreed that the last meeting would take place in the house in Najaf of Muqtada's father Mohammed Sadiq al-Sadr who had been murdered by Saddam's gunmen with two of his sons five years before. Dr Rubai'e and other mediators started for the house. As they did so they saw the US Marines open up an intense bombardment of the house and US Special Forces also heading for it. But the attack was a few minutes premature. Mr Sadr was not yet in the house and managed to escape.