The GNC, officially replaced earlier this month by a freshly-elected parliament, selected pro-Islamist Omar al-Hassi to form a "salvation government", a spokesman said.
"The GNC dismissed (interim premier) Abdullah al-Thani as head of government and gave Omar al-Hassi a week to form a salvation government," Omar Ahmidan said at a news conference in Tripoli, where GNC members met.
At the same time, Libya's new army chief declared "war on terrorists" after the elected parliament, holed up 16,000 kilometres (1,000 miles) from Tripoli in the eastern city of Tobruk, selected him to tackle unrest sweeping the nation.
The GNC meeting, for its part, gave its support for "legitimate moves aimed at liberating the country," Ahmidan said, referring to the weekend capture of Tripoli international airport by the Fajr Libya (Libyan Dawn) Islamist coalition.
Also Read
The GNC, whose re-emergence plunges Libya's rocky political transition into fresh crisis, met following a request from Islamists, who accused parliament in Tobruk of complicity in raids last week by mystery warplanes on Islamist positions near the airport.
"The meeting was illegal, its decisions are illegal and the only legislative body is parliament," Thani said in a televised news conference from Tobruk.
He said Islamist militants had ransacked and set fire to his house in Tripoli.
"The homes of many Libyans have suffered the same fate," Thani said, blaming Fajr Libya fighters.
The whole of Tripoli is unsafe and the government headquarters building has been threatened, he added.
Telling of "threats, thefts and looting" in the capital, Thani said "no public service can operate in these conditions.
"Libya cannot be ruled by force of arms. Only the police and army should have weapons," the premier said.