The group also said it was willing to drop its opposition to constitutional amendments to allow Suleiman's candidacy.
Nabih Berri, who is the parliament speaker and a key member of the March 8 opposition bloc, said the vote delay had been ordered to allow more "consensus" to be built on a presidential candidate.
Five previous sessions to elect a new president failed due to disagreements between the majority March 14 forces and the opposition March 8 bloc.
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-thirds majority.
Rula Amin, Al Jazeera's correspondent in Beirut, said that despite the agreement on Suleiman's candidacy, mistrust remains between the majority and opposition blocs.
|Opposition leader Aoun says the |
government is illegitimate [AFP]
Aoun had said he was serious about the candidacy and nomination of Suleiman but he doubted that the March 14 bloc was serious, she reported.
Aoun believes this may be a ploy to waste time and blame him for the failure to elect a president, she added.
On the March 14 side, a senior source told Al Jazeera that if the opposition was serious about electing a president, all they had to do was endorse Suleiman and amend the constitution in parliament.
The presidency of Lebanon is reserved for a Maronite Christian under Lebanon's system of allocating various leadership positions to the country's different faiths.