Al-Maliki says Iraqi police and soldiers could fill the void.
Petrol shortages across Baghdad often result in long queues at the pump.
Meanwhile, in the southern town of Sukh al-Shukh, near Nasiriya, a child and a policeman were killed when a mortar fell on a house in the centre of the town, police have said.
A woman was also wounded.
In Nasiriya, Hadi Badr, director of the Nasiriya health department, has confirmed that a roadside bomb struck a passing police patrol wounding seven policemen.
In the central city of Kut, Lieutenant Mohammed Jassim said that armed men shot dead a civilian in the al-Jamahir neighbourhood.
Jassim said the victim was part of a neighbourhood watch group that guarded the area at night to prevent attacks.
The US military has also reported the deaths of three soldiers killed by roadside bombs in Baghdad on Tuesday, taking the military’s losses since the start of the war to 3,621.