Two Shia legislators also reportedly travelled to Iran
to ask religious authorities there to intervene.
Nuri al-Maliki, Iraq's prime minister, called al-Sadr's statement "a step in the right direction".
Al-Maliki had personally supervised the operation in Basra against the militias.
"We came here [to Basra] to pursue criminal gangs and murderers ... our forces were not ready for this battle and we were surprised," he told al-Iraqiya, a state television service, on Monday.
"All those who continue to carry weapons and posses heavy weapons will be our target."
Al-Sadr's nine-point plan, agreed with the Iraqi government, was issued by his headquarters in the city of Najaf and broadcast through loudspeakers on Shia mosques.
The main elements of the plan were that al-Sadr's al-Mahdi Army forces should leave the streets in return for the Iraqi government's guarantee that it would not arrest the group's fighters unless they have arrest warrants for them, Bays said.
The deal means that Al-Sadr loyalists have kept hold of their weapons in Basra despite the best efforts of government forces to take control of the city.
Ali al-Dabbagh, an Iraqi government spokesman, told the Reuters news agency on Sunday that despite al-Sadr's order, Iraqi troops would continue military operations against "criminals" in Basra.
A curfew in place in Basra was eased on Monday to allow people out during the day, but will remain in place at night, Iraqi authorities said.
Fighting continued in the Basra area in the immediate wake of al-Sadr's announcement on Sunday, but there were no serious clashes overnight.
Seven people were killed on Sunday when a mortar struck a residential district in Baghdad's Karradah district.
Witnesses also reported clashes in the Shula area in a northern section of the capital.
The US military said it killed 25 suspected fighters in an air raid on Sunday after American ground forces came under heavy fire in predominantly Shia eastern Baghdad.
Another 16 "criminals" were also killed by US forces in a series of incidents, half of those in northeast Baghdad, US military statements said.
British forces based close to Basra's international airport were also involved on Sunday in the operation against Shia militia groups.
Tom Holloway, a British military spokesman, told Al Jazeera that British forces in Basra had fired artillery rounds at people they had identified as opposition fighters.
"We've been firing in support of Iraqi ground forces. They've been in contact, they've requested support from the coalition and artillery on a couple of occasions has been deemed the most appropriate response."
In a separate development, two US troops died in separate bombings in Iraq, the US military announced on Monday.
A soldier died when his vehicle was hit on Sunday by a roadside bomb in northern Baghdad, according to one statement.
Another statement said that a marine was "by an enemy force with an improvised explosive device" in western Anbar province on Saturday.
Source: Al Jazeera and agencies