The leaders met in Beirut at the invitation of Nabih Berri, the parliament’s speaker, who has said that unless they settled their disputes, the country would face “dangerous” destabilisation.
Hezbollah and the mainly Christian faction of Michel Aoun have called for the formation of a new coalition government and a new electoral law.
All the participants of the previous “national dialogues” attended Monday’s meeting, except Sheikh Hassan Nasrallah, Hezbollah’s leader, who sent his party’s chief legislator, Mohammed Raad, because of Israeli threats to assassinate him.
Last week, Nasrallah announced that Hezbollah wanted the cabinet to be reshuffled so his party and its allies had a third of the 24 ministerial positions, enough to effectively give them a veto.
Nasrallah said that if Fuad Siniora, the prime minister, did not grant the demand, Hezbollah supporters would stage mass demonstrations to bring down the government.
The United States has accused Syria and Iran, which support Hezbollah, of trying to topple Lebanon’s government, a charge that Syria has denied.
Siniora said Nasrallah’s demand would be discussed during this week’s talks.
Another Christian faction that supports the current government has threatened to respond with its own protests if Hezbollah supporters take to the streets.
Pro-government parties want the meeting to include discussion on the future of President Emile Lahoud, a staunch pro-Syrian whom they have been trying to remove for more than a year.
Lahoud has rejected repeated calls for him to step down.
The all-party talks began in March but have not taken place since June 25 because of Hezbollah’s 34-day war with Israel that began the following month.
In previous sessions the leaders repeatedly failed to reach agreement on Lahoud and the UN security council demand for the disarmament of Hezbollah.
The talks took place amid tight security in the capital after six people had been wounded in bombings in the capital in recent weeks.
Hundreds of police officers and soldiers cordoned off parliament causing huge traffic jams in the city centre.