Nabih Berri, parliament speaker, said the leaders agreed in four hours of closed talks on Monday to postpone the next session until April 28 "in order to decide the presidency issue, positively or negatively".
The meeting was intended to end a political crisis that has virtually paralysed the country.
If there was no agreement, he said, the leaders would move on to the last remaining - but tougher - issue of disarming the the Shia Muslim group Hezbollah.
A UN resolution calls for Hezbollah to disarm but the group, backed by Iran and Syria, has refused to do so.
Lebanon's 14 leaders - pro- and anti-Syrian, Christian and Muslim - have been trying through their unprecedented dialogue to resolve some of the most contentious issues since the end of the 1975-90 civil war.
Monday's meeting was the fifth round of talks since the national dialogue began March 2.
The talks have focused on Emile Lahoud, the Lebanese president's, fate and on a 2004 UN Security Council resolution that calls on Hezbollah and Palestinian fighters in Lebanon to disarm.
In previous sessions, anti-Syrian factions pressed for the removal of Lahoud, Damascus' top ally.
Syria's nearly three-decade military presence in Lebanon ended last April, breaking Damascus' control of the country. Since then, anti-Syrian parties have gained a majority in parliament and dominate the government.
They have accused Lahoud of being the enforcer of Syrian policy in Lebanon but they do not have the two-thirds majority in parliament needed to oust him. Lahoud, whose term ends in 2007, has rejected demands to step down.
Under Lebanon's sectarian ruling system, the president should be a Maronite Catholic, the prime minister a Sunni Muslim and the parliament speaker a Shiite Muslim.