UN special adviser on Libya Stephanie Williams urged Libyan officials to convene within 10 days to bridge the gaps between the two sides.
The talks come after clashes broke out in Tripoli between rival groups, raising fears of escalating violence in the conflict-hit country.
Gunfire and explosions rang out across Tripoli during the fighting, described by one resident as possibly the "heaviest" seen in the city for more than a decade.
Eastern parliament-appointed premier Fathi Bashaga decides to base his administration in Sirte city after an abortive bid to take the capital Tripoli by force and unseat the UN-backed Dbeibah government there.
Fighting broke out between rival groups shortly after Fathi Bashagha – appointed as prime minister by the rival government – entered the capital Tripoli.
Funerals were held across northern Lebanon for six people killed when a boat packed with migrants and asylum seekers sank over the weekend as the Lebanese navy tried to force it back to shore.
A boat carrying at least 60 people capsized off the coast of the Lebanese city of Tripoli with at least 1 child killed, 45 others rescued reportedly.
Convoys of militiamen loyal to Tobruk-parliament PM nominee Fathi Bashagha converge outside east of capital, feeding fears they would try to make violent entry into Tripoli, seat of UN-backed PM Abdulhamid Dbeibah.
UN-backed premier warns against dragging Libyans "into a new war", saying eastern-based parliament's decision to name a new premier is an attempt to take capital Tripoli by force.
UN will continue to support the unity government chief Abdul Hamid Dbeibah, spokesperson Stephane Dujarric says, after an alternative prime minister was named in a controversial vote by east-based parliament.
Libya's eastern-based lawmakers say the decision followed the failure of the incumbent Prime Minister Abdul Hamid Dbeibah to hold national elections in December.
Assailants fire several gunshots at Prime Minister Abdul Hamid Dbeibah's car in capital Tripoli before escaping from the site, media reports say.
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