Mr Maliki has come under mounting pressure since Islamic State extremist militants rampaged through the north and west of the country last month and declared a mediaeval-style caliphate on land they and other armed groups captured in Iraq and Syria.
Mr Sadr said Maliki "has involved himself and us in long security quarrels and big political crises" and suggested preventing Mr Maliki from serving a third term would be a "welcome step".
Mr Sadr added: "It is necessary to demonstrate the national and paternal spirit by aiming for a higher, wider goal from individuals and blocs and by that I mean changing the candidates." The radical cleric and his political allies had previously advocated the next prime minister be chosen from outside Mr Maliki's State of Law coalition.
State of Law is part of the National Alliance, a bloc comprising the country's biggest Shi'ite parties, including both Mr Maliki's list and his foes.
Dhiya al Asadi, secretary general of the Shi'ite political party Al Ahrar which is loyal to Mr Sadr, echoed his stance.