Contradicting an earlier announcement that his so-called National Salvation Government was ready to step aside, Tripoli's unrecognised prime minister Khalifa Ghweil urged his ministers not to stand down.
He threatened to prosecute anyone working with the new government.
"Given the requirements of public interest... you are requested to continue your mission in accordance with the law," Ghweil said in a statement.
The reason for the U-turn was not immediately clear but could suggest a split within the Tripoli authority.
There was no immediate reaction from the UN-sponsored administration of prime minister-designate Fayez al-Sarraj, which until the about-face had appeared to be cementing its control over the country's finances and institutions.
Ghweil's administration seized control of Tripoli in mid-2014 with the support of powerful militia groups, forcing a government backed by Libya's internationally recognised parliament to flee to the country's far east.
An attempt by his authority to hold on to power in the capital could spark fresh unrest in a country already struggling to emerge from five years of violence since the 2011 overthrow of Moamer Kadhafi.
Sarraj's Government of National Accord was created under a power-sharing deal agreed by rival lawmakers in December.
He arrived in Tripoli under escort by sea last week, established his headquarters at a naval base and had been moving to shore up his authority.
The international community has pleaded with Libya's warring sides to stand behind the unity government, which is seen as vital to tackling a jihadist expansion and rampant people smuggling in the North African state.
But it has not yet been endorsed by the administration based in the far east, which has long claimed international legitimacy because it was appointed by the parliament elected in the last polls in 2014.
- Winning over support -
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And the Tripoli authority's reversal will be seen as a major setback, after it had just on Tuesday issued a statement "ceasing the activities entrusted to us as an executive power" in order to "prevent bloodshed and divisions".
Sarraj's GNA had earlier on Wednesday ordered all government "ministries and institutions and committees" to respect its authority and use its logo.
It also ordered the Central Bank and the Audit Bureau to freeze all state accounts immediately, except for salary payments to government employees.
UN envoy Martin Kobler had earlier welcomed the Tripoli authority's willingness to hand over, though he had warned that "deeds must follow words".
Kobler held talks with Sarraj on Tuesday after arriving for his first visit to Tripoli since the new government arrived in the capital.
Earlier Wednesday Italian Foreign Minister Paolo Gentiloni had 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 had praised the "courage and determination" of the unity government and said the UN was ready to provide "all the support needed" towards an "immediate and peaceful handover of power".
The new administration had in recent days been broadening its support, winning the backing of the Libyan Investment Authority, the National Oil Corporation and the Central Bank.
Arturo Varvelli, a Libya specialist at the Milan-based Institute for the Study of International Politics, said the Central Bank's support was vital for Sarraj as it allows his government to "grant or stop funding... various militias".
With control of public finances, the flow of funds "can be turned on and off like a tap", he said.
Western governments are deeply concerned that Libya's disarray has allowed the jihadist Islamic State group to gain an important foothold in the country, but have said a foreign intervention can only take place at the request of a unity government.