According to Iraqi electoral commission on early Monday, Sadr's alliance with communists is closely followed by the Conquest Alliance led by former PMU commander Hadi al-Ameri.
Iraqi Prime Minister Haider al-Abadi's Victory Alliance is in third place.
The announced results are from 10 of the country's 19 provinces, including the capital Baghdad and second largest city, Basra.
Final results are expected later on Monday. Over 7,000 candidates contested 329 seats in the parliament that will choose a new president, premier and government in Iraq.
Iraqis voted on Saturday in the first national elections since the country declared complete victory over the terrorist group Daesh (also known as ISIS).
The electoral commission of Iraq announced that 44.5 percent of those eligible had cast their ballots in the elections.
