According to partial official results obtained by AFP, the Marching Towards Reform alliance of Shia cleric Moqtada Sadr and communists was ahead in six of Iraq's 18 provinces and second in four others.
So far, Prime Minister Haider al-Abadi is performing poorly in early returns, coming in third and fourth places in most provinces, and fifth in Baghdad. "We are ready to work and cooperate in forming the strongest government for Iraq that's free of corruption", Mr Al Abadi said.
Iraq's election commission says the results of the first national vote since declaring victory over the Islamic State group are expected within two days. In the years after 2003 invasion of Iraq, Sadr and the militia he controlled became a major thorn in the side of U.S. military, waging a brutal and costly insurgency against coalition troops.
A radical cleric who led militia into bloody battles with coalition forces in Iraq could now be set to run the country as his alliance edges ahead in the national elections.
Both Mr Al Sadr and Mr Al Ameri are long-time political veterans well-known to Iraqis, but both campaigned to sweep the country's reviled elite from politics.
"Hes the only politician with a clear vision for Iraq", said a Western diplomat who spoke on the condition of anonymity to give a frank assessment of Sadr. Endemic corruption has eaten at the governments financial resources. Iran has publicly stated it will not allow his bloc to govern.
Abadi - who came to power as Daesh swept across Iraq in 2014 - has been a consensus figure who balanced off the United States and Iran. No election since 2003 has had turnout below 60 per cent.
Fahmy told his party's website that Abadi's bloc was "closer" to Sadr's than others. But the vote over the weekend offered evidence that populism may be replacing sectarianism as the defining force in Iraqi politics. Instead, the bloc that wins the most seats will have to bring together a majority by getting the support of smaller alliances. Sadr portrays himself as an Iraqi nationalist and a year ago met Crown Prince Mohammed bin Salman of Saudi Arabia who is staunchly opposed to Iran.
Sadr was not a candidate for Parliament and can not himself be elected prime minister.
The Iraqi air force carried out a strike on an Islamic State (IS) position inside Syria, state television reported on Monday citing a military statement.
At the same hearing, Marine General Joseph Dunford, chairman of the Joint Chiefs of Staff, said the U.S. military learned its lesson by departing Iraq too hastily in late 2011 and allowing the Islamic State to grow.