"I would like to emphasise that these are not 'violent' clashes, at least not in our definition. They are not protracted gunfights," said U.S. military spokesman Lieutenant-Colonel Steven Stover. "While attacks continue there have been less."
Inside Sadr City, a Reuters reporter said the black-masked fighters who have long prowled the streets were keeping a low profile in response to Sadr's call for them to observe a truce.
"This morning, the Americans entered on foot from the Jamila area. We could have hit them, but we have orders to defend the city against the occupiers but not inside the city," said Abu Jassim, a Mehdi Army street commander. Outside Sadr City a Reuters reporter saw fighters planting a roadside bomb.
The government's confrontation with Sadr's Mehdi Army began a month ago when Shi'ite Prime Minister Nuri al-Maliki launched a crackdown on militias in the southern city of Basra.
Despite initial setbacks, the Basra campaign has since proved largely a success, with government troops taking control of neighbourhoods once regarded as militia strongholds.
In Sadr City, the cleric's main Baghdad stronghold, U.S. forces have advanced only into a small portion of the slum to put 107 millimetre missiles out of range of the Green Zone.
Fighting and air strikes in the district over the past month have killed hundreds. Food prices have skyrocketed and residents say they feel under siege. Many schools have shut.
Major-General Qassim Moussawi, Iraqi military spokesman for security in the capital, acknowledged civilian casualties were inevitable in fighting in a crowded slum.
"The area of this (Sadr) city is around 25 square kilometres (10 square miles) with an estimated population of 3 million. This means if a bullet is shot, it will hit a person," he said.
Um Aziz is an elderly woman whose three daughters and a son were killed when the roof of her house collapsed because of the force of an explosion nearby. She cursed U.S. forces.
"I don't want any reparations from the government. I want my revenge from God," she said outside her ruined home, wearing bandages from her own injuries and a broken leg.
"Let the Americans listen: If they kill all the men, we will fight them. We: the women and the children. And if they take our weapons we will fight them with stones and knives."
In a sign of progress towards national reconciliation, Maliki met Sunni Arab Vice President Tareq al-Hashemi to discuss the eventual return of the main Sunni Arab bloc to Maliki's government, which it quit last year.
