At the beginning of the session, Speaker Nabih Berri urged all rivals to agree on an all-inclusive solution starting with electing a new president, the media reported.
"It is a chance to reach consensus, and might be our last," Xinhua news agency quoted Berri as saying.
He warned that the sessions presented the "last of a very important opportunity to break the current deadlock and revive the state's paralysed institutions".
But the Lebanese Forces, the only party that boycotts the dialogue, dismissed it as "a waste of time".
Nevertheless, Centrist Progressive Socialist Party's leader Walid Jumblatt described the meeting as positive.
"Iran supports Lebanon's unity and dialogue and we are ready for any measure that fortifies ties between the two countries," top Iranian policy official Alaeddin Boroujerdi said.
However, expectations for feuding parties to reach understanding were low, as they have failed to elect a President and endorse an electoral law since 2014.
Lebanon has been without a president since May 25, 2014 the day former President Michel Suleiman ended his tenure.
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