The vote for provincial councils was the first election held since US troops withdrew from Iraq in late 2011, and was seen as an important test of Maliki's popularity ahead of a general election next year.
State of Law led in Baghdad, Karbala, Babil, Diwaniyah, Basra, Dhi Qar, and Muthanna provinces, and tied for first with Supreme Iraqi Islamic Council chief Ammar al-Hakim's Citizen's Coalition in Wasit.
Shiite cleric Moqtada al-Sadr's movement led in Maysan province, while local lists won the most seats in Diyala, Najaf and Salaheddin provinces.
The Citizen's Coalition came second in Najaf, Babil, Diwaniyah, Basra, Dhi Qar, Muthanna and Wasit provinces.
State of Law was second in Maysan, while Sadr's movement was runner-up in Baghdad and Karbala.
Six Iraqi provinces did not vote. The three making up the autonomous Kurdistan region are to vote later this year, as are Anbar and Nineveh, where polls were delayed because authorities said security could not be guaranteed.
Provincial council elections have not been held in Kirkuk province since 2005 because of a lack of agreement between its various ethnic groups.
An estimated 13.8 million Iraqis were eligible to vote for more than 8,000 candidates, with 378 seats being contested.