The vote cannot take place without a two-thirds quorum in parliament, which can only be secured by a deal between the ruling coalition and the opposition.
A statement from the office of Nabih Berri, speaker of Lebanon's parliament and a key opposition leader, said the next session was scheduled for January 12, at 12pm (1000GMT).
A senior political source cited "complications in regional and international negotiations and the severing of domestic talks" as reasons for another delay.
The opposition, led by Hezbollah and its allies, wants assurances it will have veto power in the new cabinet, but the majority coalition wants Suleiman elected first and says the government's formation falls within the new president's power.
Political sources said no progress was made this week in reconciling the rival camps, which blame each other for obstructing the election of Suleiman.
The presidency has been vacant since the term of Emile Lahoud, widely regarded as pro-Syrian in his outlook, ended on November 23.
The Western-backed government took measures it says are to facilitate the election of Suleiman, a 59-year-old Maronite Christian who has been army commander since 1998.
Earlier this week, the government drafted a law to amend the constitution to allow a senior public servant to be president and on Thursday, 13 parliamentarians from the ruling majority signed a petition in favour of the amendment.
Both measures were rejected by the opposition, which says no amendment is needed.
Berri has refused to accept the draft law from a government he has described as illegitimate ever since ministers from the opposition resigned from the cabinet last year.
Criticising the government's moves, Michel Aoun, the Christian leader of the opposition Free Patriotic Movement party, told reporters: "This path has enormous consequences and will hit the country's stability."
The crisis has caused deep rifts among the Christian community, who are allied to the rival political groups.
The presidency is reserved for a Maronite Christian under Lebanon's power-sharing sectarian constitution.
France, Lebanon's former colonial power, has led intensive mediation efforts, but those seem to have lost some momentum in recent days.
Suleiman, who was appointed as army chief when Syria exerted military control in Lebanon in 1998, has a positive relationship with Hezbollah, a powerful military-political group supported by Syria and Iran.