Sadr's ascendancy comes at the expense of incumbent Prime Minister Haider al-Abadi, the preferred candidate of the United States, who came in third overall.
Coming a close second in the national vote was the Fateh bloc of Hadi al-Amiri, whose Iran-backed paramilitary force played a prominent role in defeating Islamic State during years of fighting, Saeroon and Fateh each lead in four provinces out of 10.
Mr Al Abadi had been tipped as a pre-election favourite.
The vote was widely seen as a verdict on Abadi's tenure and his pledge to be more inclusive of Iraq's Sunni minority.
Mr Al Sadr himself did not run in the election, so can not be appointed prime minister, but if his bloc's results are confirmed he may be in a position to determine Iraq's next leader.
Both Sadr and Ameri are long-time political veterans well-known to Iraqis, but they pitched themselves as seeking to sweep clean the country's elite.
The ballot Saturday saw a record low turnout, as only 44.5% of eligible voters headed to the polls in the lowest participation rate since the 2003 US-led ouster of Saddam Hussein.
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Election officials said that full final results could be announced in the next 24 hours.
Reuters calculations based on the document showed Sadr had won the nationwide popular vote with more than 1.3 million votes and gained 54 of parliament's 329 seats.
The Iraqi air force has already carried out several air strikes against Islamic State in Syria since previous year, with the approval of the Syrian government of President Bashar al-Assad and the US -led coalition fighting Islamic State. A staunch nationalist, he has criticized foreign influence in Iraq and labelled the country's current political leadership as deeply corrupt. His father, highly respected Grand Ayatollah Mohammed Sadeq al-Sadr, was killed in 1999 for defying Saddam Hussein.
The surprisingly strong showing of a ticket backed by maverick Shi'ite cleric Moqtada al-Sadr in Iraqi elections over the weekend will force United States officials to recalculate how best to pursue American interests in the region at an especially sensitive moment.
Whatever the outcome, there looks to be lengthy horse-trading between the main political forces before any government can be formed.
Recent history has shown that winning a plurality of seats does not necessarily translate into gaining the premiership.
In a 2010 election, Vice President Ayad Allawi's group won the largest number of seats, albeit with a narrow margin, but he was blocked from becoming premier for which he blamed Tehran. Prime Minister Hayder Abadi's faction may be a possibility, as Sadr has said it's possible they could form a government together.