Baghdad's Sadr City is still burying its dead from the fighting
Iraqi authorities have lifted a curfew in Baghdad, allowing people to leave their homes and easing most measures put in force on Thursday.
Driving is still prohibited in three mainly Shia districts, including Sadr City, which saw some of the heaviest fighting last week.
Mehdi Army militiamen have withdrawn from the streets, residents say.
On Sunday, their leader, radical cleric Moqtada Sadr, ordered them to stop fighting Iraqi security forces.
The fighting has claimed more than 240 lives across the country since Tuesday.
The southern city of Basra, where the Iraqi army launched its campaign against the Shia militias, is also reported to be quieter, although some areas remain under the control of the Mehdi Army, and gunfire has been reported.
Another barrage of rockets or mortars hit the Green Zone complex of government and embassy buildings in Baghdad on Monday. No casualties have been reported.
In Baghdad, residents are slowly venturing out onto the streets again, with queues reported at some shops selling food and household goods.
Moqtada Sadr told followers to "work with Iraqi government offices"
The balaclava-clad, gun-toting militiamen are nowhere to be seen, reports say.
In Basra, the curfew has been lifted in daytime but will remain at night, authorities said.
Moqtada Sadr's statement on Sunday said: "Because of the religious responsibility, and to stop Iraqi blood being shed... we call for an end to armed appearances in Basra and all other provinces.
"Anyone carrying a weapon and targeting government institutions will not be one of us."
The cleric also demanded that the government apply the general amnesty law, release detainees and stop what he called illegal and random raids against his militia.
He also told his followers to "work with Iraqi government offices to achieve security and to file charges against those who have committed crimes".
The statement was welcomed by a spokesman for Iraqi Prime Minister Nouri Maliki, who warned fighters who did not withdraw would face government action.
However, Hazem al-Araji, an aide to Moqtada Sadr, told reporters that the cleric's appeal to his militias would not mean handing in weapons.
Ghazi Askar,4, is one of hundreds of Iraqis injured in the fighting
The BBC's Adam Brookes in Baghdad says this means the Mehdi Army will remain intact.
He says that although the move gives Mr Maliki a chance to claim victory, the central demand has not been met and this is not a resolution of the conflict.
The fighting began last Tuesday in Basra, when the prime minister vowed to "re-impose law" in the city.
He had then given militias until 8 April to surrender their weapons in return for cash.
The situation had appeared to be deteriorating on Saturday, with fierce fighting in both Baghdad and Basra.
Coalition forces had become more involved, with US air raids in the two cities in recent days, and British forces joining the fighting in Basra.