With Sadr's Alliance of Revolutionaries for Reform coalition [Saairun] in the lead as 16 of Iraq's 18 provinces are counted, it now appears the Shia cleric will become Iraq's main powerbroker.
The announcement came just over 24 hours after polls closed across the country amid record low voter turnout.
No single group is expected to gain an outright majority.
Sadr has reinvented himself as an anti-graft crusader after rising to prominence as a powerful militia chief whose fighters battled USA forces after the 2003 invasion.
Abadi, who is the preferred candidate of the U.S., looks set to come in third behind the Fatah (Conquest) alliance, led by former transport minister Hadi al-Amiri, who presides over the political wings of several Shia-led paramilitary forces.
After years on the sidelines, he has now reinvented himself as a crusading champion of the poor who has linked up with secularists to battle corruption. Despite a third place finish, Abadi could potentially still remain prime minister after the government coalition is formed.
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"We have tried all the others", Jamal insisted.
The protracted horse-trading ahead comes as surging tensions between the United States and Iran after Washington's withdrawal from a landmark nuclear deal with Tehran have sparked fears of a tug-of-war over Iraq.
Sadr has led two uprisings against USA forces in Iraq and is one of the few Shia leaders to distance himself from Iran.
Political sources told AFP that two meetings have been held under Iranian guidance to bring together several political blocs.
One of the alliances being suggested would see Abadi link up with the Conquest Alliance of former anti-ISIS commander Hadi al-Ameri.
Counting is still ongoing but Sadr's coalition - which is dominated by the Sadrist Movement and the Iraqi Communist Party - is believed to have won at least 54 of the 329-seat parliament, making it the largest political forces in the country, according to Al Jazeera.