UN special representative for Libya Ghassan Salame says the 5+5 commission, whose members were proposed by Libya's warring sides, will meet next week to help convert current truce into a "full-fledged ceasefire".
The four leaders agreed that attacks against civilians in Syria must stop and expressed support for a UN-backed political process in Libya.
"Mitiga airport has been targeted by fire this morning, the first day of Eid al Adha", the airport's management says in a statement.
The explosion comes hours after Libya's UN-supported government says it accepted a ceasefire proposed by the UN aimed at halting combat in the capital, Tripoli, during the upcoming Muslim holiday of Eid al Adha.
The latest territorial loss has put militia leader Khalifa Haftar in a weak position, and it is the right time for the international community to bring him to the negotiating table to help end the power struggle in Libya.
France's pursuit of its own long term interests in Libya is fueling the conflict and undermining the UN-backed peace process.
Libya's unity government was created at UN-backed talks in 2015, but it has struggled to assert control, while a number of international initiatives since have failed to unite the country.
Haftar's forces have given a strong indication that they might march on Tripoli. The international community must take diplomatic action to prevent armed conflict.
Worried about Libya turning into a source of instability on the shores of Europe, European powers have recently paid Libya more attention, and diplomats hope the two-day meeting in the Sicilian city of Palermo will keep up that interest.
Gunmen chased the car of Mayor Mohamed Eshtewi after he left Misrata airport following his arrival on a plane from Turkey, a security official said.
A month ago UN's Libya envoy Ghassan Salame announced a one-year action plan for a transition toward presidential and parliamentary elections. Since then the UN has hosted in Tunis delegations from rival parliaments from eastern Libya and Tripoli.
New roadmap proposes amending 2015 peace deal by gathering up all key Libyan actors with a national conference.
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