With most votes counted, a bloc headed by cleric Moqtada al-Sadr and another led by a militia leader are ahead, voting officials are quoted as saying.
While Sadr's unlikely Marching Towards Reform alliance with Iraq's communists looks on course to be the biggest group in parliament - it faces many obstacles. The results there, which may be delayed due to tensions between local parties, will not affect Sadr's standing.
Sadr - the former leader of the anti-Western Mahdi Army during the U.S. occupation - ran on a campaign promising to stamp out corruption but has also been keen to distance himself from Iranian influence.
After the 2003 invasion, his militia battled USA forces. "Sayyid Muqtada loves the nation, and so do I".
Regardless of the outcome of the negotiations that are bound to take place, this election has shaken Iraqi politics to the core and represents a categorical rejection of the current political class and the status quo in the country.
It is followed by a bloc linked to Iranian-backed Shia paramilitaries who fought the Islamic State (IS) group.
Al-Amiri maintains close ties to Iran. Sadr has been very critical of the presence of foreign troops in Iraq, which may have an impact on the future of United States deployments in the country. In 2014, he reorganized his fighters under the name the Peace Brigades Saraya Salam.
Meanwhile, the favourites entering the elections, Prime Minister Haider al-Abadi's Victory Alliance only managed to come first in the northern province of Nineveh, which was liberated by Iraqi forces from ISIS militants at the end of previous year. Iraqi people are likewise fed up with the USA occupation and Iranian meddling.
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On Tuesday, PM Abadi said there should be a recount if the country's new electronic system is found to be faulty.
The Reformist Shargh newspaper wrote that the surprising results of the Iraqi elections may signal a greater Saudi influence in Baghdad. Al-Abadi's Nasr (Victory) Coalition was considered the front-runner, but ended up in third place. It released the results of six more provinces late Monday.
Al-Abadi directed Iraqi forces to retake the city late a year ago after the Kurdish regional administration organized a referendum on independence that controversially included Kirkuk; federal forces moved in with little bloodshed as Kurdish forces withdrew.
Members of the election commission read out vote tallies for each candidate list in 10 provinces on national TV.
Celebrations erupted in Baghdad's Sadr City, an impoverished quarter that is home to some 3 million people and is named after the cleric's late father, Ayatollah Mohammad Sadq al-Sadr. There appears to have been a low turnout on Saturday, with Riyadh Al Badran, the electoral administration chief of the Iraqi Independent High Electoral Commission (IHEC), indicating turnout was just 44 per cent. Despite that, al-Sadr's sophisticated political machine mobilized his loyal base of followers to go to the polls.
No single group is expected to gain an outright majority. Since he did not run for a seat, he will not be eligible for the role.
Political power in Iraq is traditionally divided along sectarian lines among the offices of prime minister, president and parliament speaker.
Iranian Revolutionary Guards Quds Force commander General Qassem Soleimani was in Baghdad for talks with Shiite leaders to enforce the "Iranian choice" on the formation of a new government after the announcement of the Iraqi parliamentary election results. Almost 2,600 women ran for office this year.