The Shia parties, which won many seats in the new transitional parliament but failed to win an outright majority, have been haggling with each other over who will succed interim Prime Minister Iyad Allawi.
Secular politician and a contender for the post himself, Ahmad Chalabi of the Iraqi National Congress told reporters that a limited committee was meeting and a decision would be taken to decide from the list; refering to the list of parties and candidates of the winning United Iraqi Alliance.
The influential Shia conservative clergy-backed the United Iraqi Alliance in last month's historic elections which swept to victory, taking 140 seats in the new 275-seat parliament.
Given the list's majority, albeit slender, their choice of candidate for the prime minister's post is expected to get the job.
Former US favourite Chalabi is
also contending for the PM's post
Ibrahim al-Jafari, the current vice president and leader of Iraq's oldest Shia party, Dawa, is widely expected to get the job, while Chalabi is seen as an outside candidate.
The meeting was being held at the Baghdad offices of the Supreme Council for the Islamic Revoultion in Iraq (SCIRI), the other main party on the winning list, backed by Iraqi Shia spiritual leader Grand Ayat Allah Ali al-Sistani.
The negotiations to pick the prime minister were suspended late last week for Ashura, which marks the death in battle 1300 years ago of Prophet Muhammed's grandson al-Husain, an event which widened the split between Sunni and Shia Islam.
Attacks on Friday and Saturday during the festival left more than 70 dead.