The two days of talks in the northern port city of Tangier bring together 13 representatives each from Libya's House of Representatives (HoR) and Supreme State Council, according to participants.
Libya has been mired in violence since the 2011 fall of longtime dictator Moamer Kadhafi in a NATO-backed uprising, with an array of armed groups and two administrations vying for power.
The UN-recognised Government of National Accord dominates Tripoli and the west, while an eastern administration is backed by part of the HoR, elected in 2014 - along with military chief Khalifa Haftar.
The HoR is deeply divided, with sessions taking place in parallel in the east and west.
Following a year-long but ultimately abortive attempt by Haftar to seize Tripoli, the two sides signed a formal truce deal in October, pumping new life into UN-led efforts for a political solution to the conflict.
Mohammed Raied, an HoR member based in the western city of Misrata, said the Tangier talks aimed to "deal with pending questions such as sovereign appointments" to key posts
Last week, also in Tangier, more than 120 Libyan deputies pledged to "end the divisions" in their country, starting by convening the elected parliament as soon as they return home.
That came after a UN-sponsored political dialogue forum in Tunis in mid-November where participants agreed to hold elections on December 24, 2021, but not on who will lead the transition.