The decision means that President Fuad Masum, who Al-Maliki criticised for not intervening after parliament failed to appoint him, will now have to invite him to form a government, BBC reported Monday. The development came as pro-Maliki security forces took to the streets of Baghdad.
Al-Maliki is facing calls to step down amid a jihadist insurgency in the north region of the country.
Critics say Al-Maliki, a Shia, has precipitated the current crisis through sectarian policies. Sunnis, Kurds and even fellow Shia have urged him to leave office.
US Secretary of State John Kerry called on Al-Maliki not to increase tensions, and warned against use of force by political factions.
Al-Maliki said Sunday that he will file a legal complaint against newly-elected President Masum for violating the country's constitution.
In a nationally televised speech Sunday night, Maliki said the complaint will be submitted to the federal court as Masum did not task him and his State of Law Coalition to form the next cabinet.
Masum's attitude "is a coup on the country's constitution and political process," Maliki said, warning that "the president's deliberate violation of the constitution will have grave consequences on the unity, sovereignty, and independence of Iraq".
Masum was elected the country's new president July 24.