The polls attended by some 44.5 percent of eligible voters saw Sairun gain 54 seats, according to figures aired live by the Iraqi Kurdish Rudaw television channel.
Second-placed Fatah alliance led by ex-transport minister Hadi al-Amiri won 47 seats, while the Nasr alliance of sitting Prime Minister Haider al-Abadi came third with 42.
The winner will form a government that will rule Iraq for four years. The nation went to the polls for the first time last week since defeating the Islamic State (Daesh) terrorist group* that captured large swathes of land in 2014.
*Daesh terror organization also known as ISIL or ISIS is forbidden in US, Russia and many countries around the world.