Iraq's rival political blocs have failed to agree on important parliamentary roles, including the house's speaker, causing attempts to hold a first session of parliament in more than four months to be abandoned.

Tuesday's session was postponed indefinitely as Iraq's political process remains deadlock following election on March 7 which produced no clear winner.

"We are postponing the session until further notice because the political entities failed to reach any agreement," Fouad Massum, who as the oldest member of parliament holds the post of caretaker speaker, told a news conference.

"We held a meeting this morning with the heads of the parliamentary blocs and we agreed to give more time to political entities to reach agreement regarding the selection of a speaker and his two deputies."

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.