Politicians in areas of eastern Libya controlled by Field Marshal Khalifa Haftar on Monday said they would not take part for now in peace talks with the Tripoli government because of a UN delay in approving their representatives.
The eastern politicians said the UN, which is mediating the talks in Geneva, had not approved all members of their proposed delegation.
Their refusal is the latest blow to efforts by the world body to end the years-long conflict.
The UN had planned to bring together politicians from both sides of the conflict on Wednesday to end the fighting over Tripoli.
Its mission in Libya had said on Monday that the country's warring sides agreed to turn a shaky ceasefire into a lasting deal, bringing some hope after weeks of sporadic violence.
As the latest round of talks between rival military leaders ended in Geneva, both sides had reached a draft deal to enable "the safe return of civilians to their areas", the UN said.
The return of thousands of displaced civilians would have been monitored by military representatives in Geneva with support from the UN mission in Libya.
The delegates negotiating for Libya's rival administrations were to send the draft for approval to their leaders who have the power to halt the fighting, a prospect that faces further obstacles.
The representatives promised to reconvene in Geneva next month to work out details of the deal's implementation.
Political talks were set to begin between the two sides in Geneva on Wednesday.
Before the eastern politicians pulled out, UN envoy Ghassan Salame – who was due to meet the head of the Tripoli Government of National Accord, Fayez Al Sarraj, later on Monday – said discussions would go ahead despite continued fighting.
The ceasefire was brokered in January by Russia and Turkey, which back opposite sides in the conflict. But Libyan leaders never signed a pledge or met face to face.
A high-profile international summit followed in Berlin, where world powers promised to push for the ceasefire and uphold a widely flouted arms embargo.
But foreign backers keep pouring weapons into the country, the UN claims. Clashes continue around the capital, as each side accuses the other of breaching the ceasefire.
Nearly nine years since Nato-backed rebels overthrew Muammar Qaddafi, Libya is still without a central authority.
Forces loyal to Field Marshal Haftar said on Sunday they had killed 16 Turkish soldiers in recent weeks, a day after Turkey acknowledged it had "several martyrs" in combat operations in Libya.
Khalid Al Mahjoub, a spokesman for Field Marshal Haftar's Libyan National Army, said the Turkish soldiers died in battles in the port city of Misurata, the capitol Tripoli and the town of Al Falah, south of the capital.
Turkish President Recep Tayyip Erdogan confirmed the death of Turkish soldiers in the Libyan conflict during an address on Saturday.
"We are there with our soldiers and our teams from the Syrian National Army," Mr Erdogan said.
"We continue the struggle there. We have several martyrs. In return, however, we neutralised nearly 100 legionnaires."
Turkey backs the GNA and has sent Syrian soldiers along with some of its own and weapons to help the Tripoli-based administration repel an attempt by the LNA to capture the capital.
The Turkish soldiers and sophisticated air defences have erased small gains made by the LNA since April 2019.
Ceasefire talks between Libya's warring sides resumed on Thursday after the GNA pulled out of negotiations following the shelling of Tripoli's port by Field Marshal Haftar's forces.
