Libya's new unity government has been thrown into chaos, as the head of its rival Tripoli-based authority apparently refused to cede power.

Contradicting an earlier announcement that his National Salvation Government was ready to step aside, Tripoli's unrecognised Prime Minister Khalifa Ghweil urged his ministers not to stand down in a statement on Wednesday.

"Given the requirements of public interest... you are requested to continue your mission in accordance with the law," he said, threatening to prosecute anyone working with the new government.

Libya's UN-backed government sails into Tripoli

The reason for the U-turn was not immediately clear, but suggests a split within the Tripoli authority that seized the city two years ago, forcing out the internationally recognised government.

The move derails a United Nations push to end the instability that has ripped Libya apart for five years, one day before its envoy Martin Kobler reports to the Security Council on his progress.

Moments before Ghweil's statement, Kobler had urged a rapid and complete handover of power to the unity government, warning that a fragile peace in Tripoli may not hold if the new government were unable to deliver.

The UN envoy had also called on Libya's internationally recognised eastern parliament to hold a long-sought vote on whether to approve the UN-backed Government of National Accord, and said that the chamber risked being sidelined if it failed to do so, according to Reuters news agency.

Ghweil's administration seized Tripoli in mid-2014 with the support of powerful regional militias, forcing the government backed by the international community to flee to the country's far east.

Sarraj's Government of National Accord was created under a power-sharing deal agreed by rival politicians in December.

He arrived in Tripoli under escort by sea last week, established his headquarters at a naval base and had been moving to bolster his authority.