In a statement, Parliamentary Secretary-General Adnan Daher said another attempt would be made on January 17.
Two thirds of the assembly must be in attendance for the vote to be considered constitutional.
The Lebanese presidency has remained vacant since Suleiman's six-year term expired in May.
Parliament has so far been unable to elect a new president, with MPs from the Hezbollah-led March 8 alliance consistently boycotting the assembly vote.
The alliance has refrained from officially backing either of the two candidates to have expressed an interest in assuming the post, namely Lebanese Forces leader Samir Geagea and MP Henri Helou.
The political deadlock comes as the ongoing conflict in next-door Syria continues to fuel sectarian tension inside Lebanon, where Shiite Hezbollah's military support for the Syrian regime has drawn condemnation from local Sunni groups.