The Lebanese parliament was due to meet on Friday to elect a successor to Emile Lahoud, whose term expired last week, but the vote has now been postponed to December 7.
Nabih Berri, who is the parliament speaker and a key member of the March 8 opposition bloc, said the delay had been ordered to allow more "consensus" to be built on a presidential candidate.
Five previous sessions to elect a new president have failed due to disagreements between the majority March 14 Forces and the opposition March 8 bloc.
The March 14 bloc is supported by the West while the opposition draws support from Iran and Syria.
Hezbollah, which leads the opposition, had declared that it would only consider Suleiman to be a consensus candidate if Aoun accepted.
Now that Aoun has declared he would support Suleiman's candidacy, the focus will shift towards whether an agreement can be reached between the rival political factions on constitutional amendments.
Aoun and the rest of the opposition have branded the March 14 government as illegitimate since members of the opposition bloc pulled all their ministers out of the cabinet last year, citing a lack of veto rights in cabinet decisions.
"There are constitutional obstacles that should be removed because the government is illegitimate," Aoun said.
"The parliament, according also to the constitution is only an electoral body now - it cannot change the constitution."
In previous amendments, parliament had to ratify government recommendations by a two-third majority.
Rula Amin, Al Jazeera's correspondent in Beirut, said mistrust remained between the majority and opposition blocs.
"Michel Aoun said he is serious about the candidacy and nomination of Suleiman but he doubts that March 14 are serious," she said.
"[Aoun] believes this may be a ploy to waste time and blame him for the failure to elect a president."
Amin said that March 14 is considering the latest developments to be crucial in the presidential election process.
"We heard from a very senior source in March 14 that this is the moment of truth and that if the opposition is serious about electing a president... all they have to do is endorse Michel Suleiman, go to the parliament and amend the constitution. Then Lebanon will have a new president."
The presidency of Lebanon is reserved for a Maronite Christian under Lebanon's confessional system.