According to BBC reports, the announcement comes less than a week after the arrival in Tripoli of a UN-backed national unity government.
The Tripoli-based administration said it was standing down to prevent further bloodshed.
Since 2014 Libya has had two competing administrations, the one in Tripoli backed by powerful militias and the other in the eastern city of Tobruk.
The Tobruk-based administration, formed by the House of Representatives, still opposes the UN-backed body. BBC reports.
"We inform you that we are stopping our work as an executive power, as the presidency and ministers of the government," said the statement by the self-declared National Salvation government.
The UN-brokered unity government arrived in Tripoli last week and is now operating from the city's naval base as it strives to restore peace in a country ravaged by factional conflict.
Western countries want the unity government to unite as many factions in Libya as possible against an increasingly powerful affiliate of the group known as Islamic State.