Russian FM Lavrov says Fayez al Sarraj and Khaled al Mechri "have just signed" the ceasefire agreement, while Khalifa Haftar and Aguila Saleh "have asked for a bit more time until morning to make a decision on its signing."
Russian Foreign Minister Sergey Lavrov has said Monday's talks on a ceasefire deal between the warring sides in Libya had made some progress, but warlord Khalifa Haftar asked for more time to study the document.
Warlord Haftar's militia based in eastern Libya have been battling since April to take Tripoli from the UN-recognised government in the capital.
The Moscow talks followed a joint call by Turkish President Recep Tayyip Erdogan and President Vladimir Putin for a ceasefire in the North African state.
"There has been certain progress" after talks in Moscow with Russia and Turkey lasting some seven hours, Lavrov told journalists in a short statement.
He said the head of Libya's UN-recognised Government of National Accord (GNA) Fayez al Sarraj and head of High Council of State in Tripoli, Khaled al Mechri "have just signed" the ceasefire agreement.
But Haftar and Aguila Saleh, a Haftar ally, "have asked for a bit more time until morning to make a decision on its signing," Lavrov said, though claiming they also "view the document positively."
Ankara and Moscow have established themselves as key players in Libya.
The ceasefire document spells out the terms of a ceasefire which took effect over the weekend.
Turkish Foreign Minister Mevlut Cavusoglu said once the document is signed by Haftar, both sides "would take the responsibility" for a ceasefire launching a political process in the country.
Turkey and Italy urge permanent ceasefire in Libya
Turkish President Erdogan and Italian Prime Minister Giuseppe Conte called for a permanent ceasefire in Libya following a meeting in Ankara on Monday.
"We are exerting efforts for the ceasefire to be permanent," Erdogan said in a televised press conference a day after a fragile ceasefire was established.
"We have discussed the urgent necessity of putting an end to the escalation on the ground to guarantee a lasting ceasefire," Conte said.
"The ceasefire might result in a precarious measure if it isn't included in a larger collective effort of the international community aimed at guaranteeing the unity, stability, sovereignty of Libya," he added.
Erdogan said he hoped United Nations forces would help enforce the ceasefire.
"Right now talks are continuing in Moscow," he said. "I have information from my friends a while ago that the talks are continuing in a positive direction.
"I think it will be the right move if the UN is tasked as an observer to strongly maintain the peace process."
Erdogan and Conte were meeting as the heads of Libya's warring parties came together in Russia, where they were expected to sign an agreement ahead of an international summit due later this month in Berlin.
Russia is hosting a meeting of Libya's rival leaders on Monday — a mediation effort closely coordinated with Turkey.
The Russian Foreign Ministry said that Sarraj and Haftar will meet for talks in Moscow.
The negotiations follow a ceasefire proposed by Russia and Turkey that began Sunday — the first break in fighting in months. There were immediate reports of violations by both sides, however, raising concerns it might not hold.
The ceasefire came as Libya's civil war was on the brink of a major escalation. Various foreign players back Libya's two rival governments, and they have recently been stepping up their involvement in the oil-rich nation's conflict.
Libya plunged into turmoil after the 2011 civil war that ousted and killed long-time leader Muammar Gaddafi.
Haftar is supported by France, Russia and key Arab countries, including Egypt, the United Arab Emirates and Saudi Arabia.
Turkey, Italy and Qatar support the UN-recognised Tripoli government, which has faced an offensive by Haftar's militia, which closed in on the capital.
Russian President Putin discussed the situation in Libya with German Chancellor Angela Merkel, who visited Moscow on Saturday. The Russian leader welcomed Germany's plan to hold a Libya peace summit in Berlin early this year.
On Sunday, Putin also discussed Libya in phone calls with French President Emmanuel Macron and Italian Prime Minister Conte. The Kremlin said they emphasised the need to respect the ceasefire that took effect Sunday and spoke in support of the planned summit in Berlin.
Russia has maintained contacts with both conflicting parties in Libya, but the government in Tripoli has recently charged that Russian military contractors were fighting alongside Haftar.
Asked Saturday about Russian private security companies in Libya, Putin responded that “if there are Russian citizens there, they do not represent the interests of the Russian state and do not receive any money from the Russian state.”
The Russian president noted that mercenaries were sent to Libya from Syria's opposition-held province of Idlib alongside Turkey's border, voicing hope that a lasting ceasefire will help end the deployment of foreign fighters to Libya.
Erdogan said earlier this month that his country was sending military personnel to Libya to support Sarraj's government. Sarraj visited Istanbul for talks with Erdogan on Sunday before heading to Moscow.