The concession late yesterday by the militia-backed administration that had controlled Tripoli since 2014 was a major about-turn for a body that had made every effort to block the arrival of prime minister-designate Fayez al-Sarraj.
It came after UN envoy Martin Kobler held talks with Sarraj at the naval base where he has established his headquarters since his arrival under escort by sea last Wednesday.
The international community has pleaded with Libya's warring sides to stand behind the unity government, which it sees as vital to tackling a jihadist expansion and rampant people smuggling in the North African state.
In a directive published on its official Facebook page today, the GNA ordered all government "ministries and institutions and committees" to respect its authority and use its logo.
Also Read
It also ordered the Central Bank and the Audit Bureau to freeze all state accounts immediately, except for salary payments to government employees.
The Tripoli-based administration had said it was stepping aside in the national interest.
The statement, bearing the logo of the so-called National Salvation Government headed by Khalifa Ghweil, said the unrecognised Tripoli prime minister, his deputy premiers and cabinet ministers were all stepping aside.
It said the Tripoli authorities took the decision to quit because they were determined to "preserve the higher interests of the country and prevent bloodshed and divisions."
Italian Foreign Minister Paolo Gentiloni said recent developments were "encouraging" in moving towards a "united, stable and secure Libya".
"I hope that the spirit of compromise prevails on all parties involved," he said in a statement, offering the full support of Italy, the former colonial power in Libya, to the new government.
Kobler praised the "courage and determination" of the unity government, whose growing authority has raised hopes it will be able to restore some stability in Libya, which has been plagued by chaos since Moamer Kadhafi's 2011 overthrow.