“I’m resigning because I have failed,” said a visibly moved Kouni, who is originally from southern Libya and represents the Tuareg minority in the GNA.
“We (in the GNA) are responsible because we accepted this mission.
“We take responsibility for everything that has happened in the past year: dramas, violence, murder, rape, invasion, the squandering of public funds… Regardless of the extent of the crimes, we are responsible,” he said.
Libya has been mired in chaos since the 2011 downfall of longtime dictator Muammar Gaddafi.
In March last year, the internationally backed GNA was formed, intended to replace two rival administrations, one in Tripoli and one in the country’s far east.
It is also the centrepiece of Western hopes to stem an upsurge of jihadism in Libya and halt people trafficking across the Mediterranean that has led to thousands of drownings.
Jihadists of the Islamic State group have been chased from their North African stronghold in Sirte 450 kilometres (280 miles) east of Tripoli after eight months of deadly fighting.
Despite this success, the GNA has failed to assert its authority fully over the whole country.
Prime minister-designate Fayez al-Sarraj has not yet been able to secure a vote of confidence in the Libyan parliament based in Tobruk in the east, where the military leader of the parallel authorities, Marshal Khalifa Haftar, is also based.
“The inability to meet people’s expectations leads me to resign… I pledged to alleviate their suffering but I did not succeed,” Kouni also wrote on his Twitter account.