BAGHDAD, Iraq (CNN) -- A U.S. military official said Sunday it was "premature" to conclude there will be a truce between the Iraqi government and Shiite cleric Muqtada al-Sadr's movement, despite word from both sides that a cease-fire agreement was reached.
A U.S. Army soldier walks past Iraqi armored vehicles after returning from a Sadr City operation Sunday.
"Yesterday, we did see a dialogue, and it's important to emphasize that it's an ongoing dialogue process and we're waiting to see the details being worked out and implemented today," said Rear Adm. Patrick Driscoll, a spokesman for the U.S.-led multinational forces.
"We welcome an end to violence and putting an end to the criminal activity, so we are obviously in support of the government of Iraq as they move forward in a dialogue with elements of the Sadr trend."
Spokesmen for the Iraqi government and al-Sadr's movement announced the cease-fire agreement Saturday. The United States is not party to the discussions.
The 14-point agreement will "impose the state's authority and security ... in Sadr City," Iraqi government spokesman Ali al-Dabbagh said.
It will end the militias' armed presence in the sprawling eastern Baghdad slum, he said, and clear the district of roadside bombs and mines that the United Nations Children's Fund says have rendered many roads inaccessible.
Sheikh Salah al-Obeidi, an al-Sadr spokesman, told CNN the cease-fire would go into effect no later than Sunday morning.
It was unclear who would abide by the cease-fire. Not all Shiite militants involved in the Sadr City fighting are members of al-Sadr's Mehdi Army. The U.S. military has said the Shiite militias in Sadr City are Iranian-backed cells that have not obeyed al-Sadr's freeze of Mehdi Army military activities. The cleric put the freeze in place in August and renewed it in February.
Iran denies backing violent groups in Iraq.
Driscoll said some limited operations continued Sunday in Sadr City. The Iraqi military has been leading operations in the area, backed by the U.S. military.
Sadr City residents said things were relatively calm Sunday, following weeks of fighting. After receiving dead and wounded people daily, Sadr Hospital said Sunday it received no casualties. The other main hospital, Imam Ali Hospital, said about a dozen wounded were admitted.
Iraqi and U.S. forces have battled Shiite militants in Sadr City since the end of March. About about 1,000 militants and civilians have been killed in fighting, and more than 2,000 have been wounded.
Negotiations between the Iraqi government and Sadrists began a few days ago, al-Obeidi said. The United Iraq Alliance, the ruling Shiite political bloc of which Prime Minister Nuri al-Maliki is a member, mediated, he said.
Following the cease-fire, the government will reopen all entrances to Sadr City, allowing necessary aid to flow in and the wounded to be evacuated, al-Obeidi said. Access to the district has been limited during the military operations, and there are shortages of water, food and medical supplies there, according to UNICEF.
Iraqi security forces will maintain checkpoints at the entrances of Sadr City to prevent any infiltration, al-Dabbagh said.
Iraqi forces will also be on the district's streets, conducting searches and raids to detain wanted individuals, according to al-Obeidi, and he warned that according to the agreement, the government will punish the security forces if they violate residents' rights in the process.
On Saturday, the Mehdi Army distributed among its members a statement telling "brothers in the Mehdi Army" to hold their positions until they receive another statement from the Mehdi command.
"When you hear news of agreements or negotiations, and even if news channels and stations broadcast news about a withdrawal or something of the sort, you have to stand firm and not abandon your positions until you hear another statement from the Imam Mehdi Army's command," the statement said.
"Be aware that the enemy's propaganda controls all channels and satellites, and in one way or another they are trying to affect our determination and morale," it said.
While Sadr City hoped for a change, it was a bloody Sunday in northern Iraq. Four people, including a woman and a child, were killed when coalition forces fired into a car south of Mosul, the military said Sunday.
Troops fired when the driver of the car refused to stop for a vehicle check, a U.S. military news release said.
The military said it sincerely regrets when civilians are killed during its operations to "rid Iraq of terrorists."
At the time, troops were looking for associates of foreign al Qaeda fighters, the military said.
Iraqi and U.S. troops have stepped up operations in recent months against al Qaeda in Iraq in Nineveh's provincial capital of Mosul, a predominantly Sunni city and one of Iraq's most dangerous.
Al-Maliki -- who has been focused lately on the troubles in the Shiite regions of Iraq -- deployed more Iraqi troops to Mosul and the surrounding province earlier this year. He had promised an offensive to root out the insurgency there.
CNN's Jomana Karadsheh and Christine Theodorou contributed to this report.