Libya's warring sides have begun to engage in a new round of ceasefire talks, the United Nations said on Wednesday, after rapid gains by the internationally recognised government ended with heavy fighting around the central coastal city of Sirte.

The Government of National Accord (GNA), which is backed by Turkey, and the eastern-based Libyan National Army (LNA), backed by the United Arab Emirates, Russia and Egypt, have each met separately with UN negotiators, the UN Libya mission said.

It follows the sudden collapse of the LNA's 14-month offensive to capture the capital Tripoli, the seat of the GNA, and its retreat from most of its territory in northwest Libya.

A GNA effort from Monday to push further east and capture Sirte, effectively wiping out all the LNA's gains since the start of its Tripoli campaign in April 2019, was repulsed with air strikes, an LNA military source said.

"The Mission is particularly concerned by reports of escalation and mobilization in and around the city of Sirte", the UN Libya mission said in its statement announcing the talks were under way.

It said it had verified at least 19 civilian deaths in Sirte.

Libya's warlord Haftar on Wednesday met with a German envoy amid renewed international efforts to end the years-long conflict in the North African country.

The meeting between German Ambassador Oliver Owcza and Haftar came days after Egypt unveiled a plan, including a ceasefire, to end the war in neighbouring Libya.

The proposed truce was supposed to go into effect on Monday, though there has been no direct reply to the plan, backed by Haftar, from his rivals in the internationally recognized Government of the National Accord (GNA) based in Tripoli.

Haftar met Owcza near Libya's eastern city of Benghazi.

The German diplomat said that during his meeting with Haftar he voiced concern about ongoing military confrontations in Libya and their impact on civilians.

"I encouraged a constructive resumption of 5+5 talks towards a reliable ceasefire, thereby also addressing structural security concerns," Owcza tweeted, referring to UN-sponsored military talks.

Last week, the GNA's forces regained control of several bordering areas of Tripoli, foiling a months-long campaign by Haftar to seize the city.

Haftar's forces also lost control of Tarhouna, his last stronghold in western Libya.

Oil-wealthy Libya has been in turmoil since a 2011 revolt toppled long-time dictator Moamer Gaddafi and has become a battleground for rival proxy forces.

Turkish President Recep Tayyip Erdogan also on Wednesday discussed in a phone call with his Russian counterpart Vladimir Putin "regional issues, including particularly developments in Libya," Erdogan's office said without elaborating.

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