"This session is adjourned, and it will be held next week in the event of an agreement," Mehdi al-Hafidh told lawmakers.
Parliament convened with 255 deputies out of 328, but only 75 returned after a recess to discuss candidates.
The parliament was due to elect a new president after confirming the speaker.
The president would then charge the leader of the biggest parliamentary bloc with forming a government as prime minister.