Sadr said in Najaf Tuesday Maliki is asserting greater control over the government, monopolizing power and cracking down on opponents.
Sadr said he supports widespread, peaceful protests as long as they do not seek to create divisions.
The New York Times said Sadr's comments could indicate he is testing the waters for the provincial elections this spring.
The Times said demonstrations against Maliki began in Sunni areas last month after security forces raided the home of Sunni Finance Minister Rafia al-Issawi and arrested 10 of his bodyguards.
The Times said tens of thousands of Sunni Muslims participated in one protest last week, in which they blocked Iraq's main trade route to Syria.
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