The group, the Iraqi Accordance Front, blames the Shia-led government for not protecting Sunni mosques in a wave of violence following Wednesday's bombing of a Shia shrine in Samarra.
Iyad al-Samarrai, a member of the front, said: "The government neglected to provide security for our sites... They did not condemn these acts of aggression."
Iraqi police said dozens of people, mostly Sunnis, were killed in Baghdad and elsewhere in the 24 hours after the bombing of the Askariya shrine.
Dozens of Sunni mosques were attacked and Shia militias took to the streets.
The meeting was meant to start at 10.30am (0730 GMT), but officials later said it would take place in the afternoon because the main Shia alliance, which dominates the interim government, was holding an internal meeting in the morning.
It was not clear if broader talks would go ahead without the Accordance Front, which includes the Iraqi Islamic party.
The front won 44 of 275 seats when the once dominant Sunni group ended its boycott of the US-sponsored political process and took part in an election in December.