Libya's rival leaders have left Moscow without reaching agreement on a ceasefire deal proposed by Russia and Turkey in an effort to bring an end to the country's long-running civil war.

Fayez Sarraj, the head of Libya's UN-recognised government in Tripoli, and his rival Hafter came to Moscow on Monday to discuss a truce with top diplomats and military officials from Russia and Turkey, although they did not meet directly.

After the meetings, Russian foreign minister Sergey Lavrov and his Turkish counterpart, Mevlut Cavusoglu, announced that Sarraj had signed the draft document spelling out the details of the proposed ceasefire deal, while Hafter requested more time to consider it.

But on Tuesday morning, Russia's foreign ministry said Hafter had left Moscow without signing the deal. Russian news agencies reported that Sarraj had also left.

Russia's defence ministry put out a statement saying that Hafter could still sign the proposed draft and Lavrov said that efforts to broker a peace deal will continue.

But Turkey's leader Erdogan said on Tuesday his country will not refrain from "teaching a lesson" to Haftar if his forces continue attacks against the internationally recognised government in Tripoli.

Erdogan said Haftar had "run away" from the talks and told the Turkish parliament If the attacks continued "we will never refrain from teaching him the lesson he deserves."

Erdogan added: "It is our duty to protect our kin in Libya."

Later on Tuesday, Germany confirmed it will host a conference on Sunday in Berlin to support the United Nations' efforts to achieve a peaceful resolution to the conflict.

Representatives from the US, Russia, Britain, France, China, Turkey, Italy and the UN will be among the participants, said the German government in a statement.

Germany also confirmed it has invited Serraj and General Haftar to the talks.

Australian Associated Press