A group of protesters said it would occupy city streets and squares until all the ruling political bodies "announce their resignation in public".
UN-backed government leader Dbeibah added that he agrees all the government institutions should leave and supports protesters in the country.
Libyan legislative leaders have quit talks in Geneva on a constitution and elections without reaching a deal, pausing diplomacy to resolve a standoff that has imperilled a two-year peace process.
Special representatives of the neighbouring countries will convene in Vienna to discuss steps towards rapprochement.
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.
The cause of the violence in the seaside neighborhood was unclear, but videos circulated on social media showed families with children sheltering and fleeing as artillery fire flew across the night sky.
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.
Fourteen members of the UN Security Council voted to resume arm and munition transfers to Libya for one more year while Russia abstained.
Boat carrying around 100 migrants and refugees capsizes off the port of Sfax, with the coastguard and navy units able to pull 24 people out of the water, Tunisian officials say.
Thirty-one-year-old Mohamed Alnaas will receive $50,000 as prize money for his debut novel, "Bread on Uncle Milad's Table", which explores gender roles in a Libyan village.
Growing regional ties and cooperation are leading rapid economic recovery for Algeria and Türkiye, despite nearly two years of pandemic disruption and market volatility.
Subscribe to our Youtube channel for all latest in-depth, on the ground reporting from around the world.
Copyright © 2022 TRT World.