The meeting in Irbil in Iraqi Kurdistan is the first public gathering to include the two main rivals -- Prime Minister Nouri al-Maliki and former Prime Minister Iyad Allawi -- since the March 7 elections left no clear victor, CNN reported.
The opening addresses of the three-day talks, hosted by Kurdish regional President Massoud Barzani, were broadcast live.
Last month, Barzani proposed having the blocs hold roundtable talks to achieve the long-delayed formation of a government.
Maliki won 89 seats in the election while Allawi's bloc took 91. A 163-seat majority out of 325 seats is needed.
Before Monday's meeting, officials had said they were close to an accord. But Sunni Vice President Tariq al-Hashimi, an Allawi ally, said the preliminary meetings had not tackled the toughest issues.
Allawi's al-Iraqiyya and other smaller blocs oppose a second term for Maliki.
Maliki last month joined forces with Shiite cleric Moqtada Sadr and one of the smaller Sunni Arab groups. The Kurdish coalition, with more than 50 seats, has also hinted at endorsing him.
Notable deaths of 2014 [PHOTOS]