Militants were withdrawing from the streets and shops were reopening in Baghdad's Sadr City on the first day of a cease-fire between Shiite extremists and U.S.-backed Iraqi forces following two months of intense clashes.

Authorities reported no violence Sunday.

"Today, people are very happy and very optimistic," said Sadiq Jaafar, a 30-year-old father. "Last night for the first time in more than 40 days we were able to sleep without being woken up by explosions or gunfire."

U.S. military officials said at a news conference Sunday that the Iraqi government was still working out details of the truce with elements of the Sadrist movement of anti-American cleric Muqtada al-Sadr.

"It is important to emphasize that it is an ongoing dialogue process," said U.S. military spokesman Rear Adm. Patrick Driscoll. "It is premature to say there is an agreed to truce."

The U.S. military has repeatedly emphasized that the clashes are being carried out by rogue elements and groups that have splintered from al-Sadr's Mahdi Army.

There was no immediate comment Sunday from the Iraqi government and its spokesman was unavailable Sunday. But the government has said it retains the right to chase wanted militants and search houses in order to confiscate weapons.

Thousands of civilians have fled their homes in the teeming slum — home to nearly 40 percent of Baghdad's population — and aid groups said some areas are desperately short of food and medicine after seven weeks of street battles.

Followers of al-Sadr, who was apparently instrumental in brokering the cease-fire, distributed food in the neighborhood Sunday, residents said.

The bulk of al-Sadr's 60,000-strong Mahdi Army is not believed to have participated in the clashes, instead adhering to a general cease-fire ordered by al-Sadr last August. The violence is blamed on splinter groups believed to be acting on their own. Al-Sadr has directed his supporters to only fight when attacked.

Prime Minister Nouri Al-Maliki has called on al-Sadr to disband the Mahdi Army and vowed to disarm its members.

"We have concerns about this agreement," a senior commander of the Mahdi Army, speaking on condition of anonymity for security reasons, said Sunday. "When U.S.-led forces enter the area, we fear that they will pursue us."

The commander spoke by telephone from the most troubled southern part of the district, where U.S. and Iraqi forces are building a barrier — reaching up to 12 feet high — to isolate it and disrupt supply and escape routes for militants.

During the clashes, Shiite extremists fired rockets or mortars from the area toward the heavily fortified Green Zone, housing the U.S. embassy and much of the Iraqi government offices. They often fell short, killing or wounding civilians in downtown Baghdad.

The latest conflict flared in late March after al-Maliki ordered a crackdown on armed Shiite factions in the southern city of Basra, the nation's second-largest urban area. Mahdi fighters quickly rose up in Basra and Sadr City, their stronghold in Baghdad.

Meanwhile, the U.S. military on Sunday said four people, including a woman and a child, were killed in an operation against al-Qaida in Iraq near the northern city of Mosul on Saturday.

The military regretted killing "civilians" in the operation against what was described as associates of foreign al-Qaida fighters. The woman and the child were riding in the same vehicle with the gunmen, it said.

Iraq's security forces on Saturday launched a new operation against al-Qaida in Mosul, which was considered the last important urban staging ground for al-Qaida in Iraq after losing its strongholds in Baghdad and other areas during the U.S. troop "surge" last year.

About 140 people have been arrested in raids and some 120 roadside bombs were seized in a house in western Mosul, a police official, speaking on condition of anonymity because he was not authorized to speak to the media, said Sunday.

The military on Sunday also announced that one U.S. soldier was killed when the vehicle he was traveling in rolled over near al-Asad, home to the second largest air base in Iraq.