Influential cleric Moqtada al-Sadr's bloc won the most seats, while Badr Brigade head Hadi al-Amiri came in a close second.
The partial results are a severe blow to incumbent Prime Minister Haider al-Abadi, whose Victory Alliance [al-Nasr] is now third in the polls, according to partial results.
Populist Shiite religious scholar Moqtada Sadr Tuesday eyed a governing coalition after dealing a blow to both Iranian and US influence with a shock election triumph that upended Iraqi politics.
He announced Tuesday on state television that it was the responsibility of Iraq's Independent High Electoral Commission (IHEC) to conduct the recount to determine accurate results, citing high-profile charges of vote tampering in the disputed province of Kirkuk.
Although al-Sadr won't be prime minister because he himself didn't run in the election, he will have the power to name the next leader-and this could seriously influence Iraq's politics and policies.
Despite the election setback, Abadi might still be granted a second term in office by parliament and on Monday he called on all political blocs to respect the results and suggested he was willing to work with Sadr to form a government.
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Mr Al Sadr made a concerted effort to appeal to marginalised and disillusioned Iraqis while styling himself as a reformist leader determined to effect comprehensive change to a failing political class.
While speculation swirls, the next concrete step remains completing the vote count and firming up the final makeup of Iraq's new 329-seat parliament.
Voter turnout was at a low 44 percent, 15 percent lower than the turnout in the 2014 parliamentary elections. It included full returns from only 10 of the country's 19 provinces, including the provinces of Baghdad and Basra.
"His visit coincided with the announcement of the election results". Of more than 2 million Iraqis displaced by the war, the majority are Sunnis. Former Prime Minister Nuri al-Maliki, a close ally of Iran like Amiri, came in fourth with around 25 seats.
Political sources told AFP that two meetings have been held under Iranian guidance to bring together several political blocs.