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.
Eighty-nine of 113 lawmakers present in eastern city of Tobruk vote to withdraw confidence from Tripoli-based administration of interim PM Abdul Hamid Dbeibah.
Sarraj’s resignation might be designed to pave the way for a new reconciliation process between the Tripoli government and the Tobruk-based eastern political forces.
Experts say the Tobruk-based government's resignation erodes warlord Khalifa Haftar's political leverage against the internationally recognised Libyan government.
The agreement between the UN-recognised government in Tripoli and the Tobruk-based legislature to demilitarise Sirte is an important step towards peace but obstacles remain primarily in the form of the renegade warlord, Khalifa Haftar.
The truce aims to make Sirte a temporary seat for a new presidential council to be guarded by police forces from various regions in the country.
Libya's army shared images of military equipment in Tobruk which it said arrived from Egypt the same day the US military posted photographs of landmines used by Kremlin-backed Wagner Group in Tripoli to support Haftar.
The warlord general announced a new government in Libya to counter the UN-recognised government led by Prime Minister Fayez al Sarraj.
Pro-Haftar mercenaries were also deployed to the region and drones operated by the United Arab Emirates were flying over Tripoli.
Turkey’s deal with Libya’s UN-recognised government in Tripoli is a signal to other Mediterranean states that Ankara can block their gas routes.
Turkey's support to the UN-backed Government of National Accord in Libya should be replicated by other responsible global powers.
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