The first attempt to hold a parliamentary session, on June 14, was adjourned after only 20 minutes.
The country's main political groups have been unable to strike a coalition deal.
The Iraqiya bloc, led by Iyad Allawi, a former prime minister, finished first in the election with 91 seats, followed closely by the State of Law alliance, led by Nouri al-Maliki, the incumbent prime minister, with 89.
The Iraqi National Alliance, a group of Shia Muslim parties, finished third with 70 seats.
Al-Maliki has joined with the National Iraqi Alliance to form a larger coalition but the new union still does not have enough seats in the 325-seat parliament to get a majority.
Both al-Maliki and Allawi are claiming the post as prime minister.