Current prime minister Haider al-Abadi, who is supported by the United States, Tuesday said that if a new electronic voting system used in the election was found to be faulty, the election commission should hold a nationwide recount, state television reported.
Iraqi election officials announced on Monday that Muqtada al-Sadr, the Shiite cleric and militia leader, is the front-runner in the country's national elections.
Abadi, who is the preferred candidate of the USA, 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.
Sadr's gains have called into question the presence of USA forces in Iraq, where more than 5,000 troops are indefinitely deployed to prevent a resurgence of the Islamic State group.
The race to become Iraq's next prime minister appears wide open as Muqtada al Sadr's alliance looked to be in the lead after the first elections since the defeat of Daesh.
Meanwhile, allegations of vote rigging in northern Iraq were delaying final results on Tuesday, with some Kurdish parties demanding a re-run of the weekend's poll.
As Kurdistan 24 points out, al-Sadr has "far fewer ties to Tehran than Soleimani's clear preferred victor, Al-Fatih Coalition leader Hadi al-Amiri", which is likely the reason for Soleimani's visit-to form Iraq's next government.
Al-Sadr's list is leading the popular vote count, followed by a list linked to Iraq's predominantly Shiite paramilitary forces that fought alongside Iraq's army in the war against IS militants.
"I can just say the independent high electoral commission - that's basically the Iraqi equivalent of the federal election commission - they are investigating". The elections were held Saturday, with low turnout.
"The Iraqi people had an election".
The remaining uncounted ballots, mostly from Iraqis overseas, the security services, and internally displaced people voting in camps and elsewhere, might change the final seat tallies but only marginally.
Saturday's election is the first since the defeat of ISIL a year ago.
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.