The talks should establish a timetable and an agenda for future meetings.
Al Jazeera's Sherine Tadros, in Baabda, said: "[It] is the beginning of a discussion on how Hezbollah and the Lebanese state can co-exist."
Tadros said: "It is a much wider discussion than simply how to disarm Hezbollah. Hezbollah have already said that it will not disarm as long as there is a threat to the Lebanese state."
|President Michel Sleiman heads the talks between 14 leading politicians [AFP]
Analysts believe that Hezbollah will not bend to disarmament demands in view of its dominant position. The group is expected to attempt to expand the number of its allies in the talks with the parliamentary majority dominating.
Saad al-Hariri, the parliamentary leader, said: "Expanding the dialogue is a tactic to buy time and determine the outcome in advance."
Hezbollah's arms are a sticking point. The group, backed by Iran and Syria, argues that its weaponry is needed to protect the country from Israeli attacks.
The parliamentary majority, backed by Western nations, asserts that the state should be the only body with responsibility for issues of national security.
Therefore, Tadros said: "This is about co-existance rather than simply trying to take Hezbollah's arms.
"A Hezbollah official in the south did say on Monday night that they were ready to begin discussions on how there could be a complimentary relationship between Hezbollah fighters and the Lebanese army."
Tadros said that Walid Jumblatt, a prominent member of the March 14 group, said on Monday that he was ready for the state to utilise Hezbollah's military power.
She said: "That is a very significant change in the language that we have seen in the past."
The talks are an outcome of the Doha peace accord signed in May, immediately after street battles between fighters loyal to the political rivals killed 65 people.
The accord curtailed 18 months of deadlock, during which the sides were unable to agree on a new president. Sleiman was eventually appointed and the formation of a national unity government went ahead.
However, the country has seen sporadic incidences of violence since.
On Tuesday morning, one person was shot dead and another two wounded in the split Sunni and Shia village of Taalbaya Bekaa Valley region in eastern Lebanon.
In June, three people were killed in the same region in clashes between supporters of Hezbollah and the Future Movement, a rival faction.