Libya plunged into chaos after a 2011 Nato-backed uprising toppled and killed veteran dictator Moamer Kadhafi, with heavily armed former rebels carving out their own fiefdoms across the country.
Two parliaments and two governments are vying for control of the country, where the Islamic State jihadist group has recently made inroads.
Months of UN-mediated talks between Libyan factions have failed to produce a political accord.
On Monday, members of the rival parliaments return to Morocco for a new round of peace talks.
UN envoy Bernardino Leon is scrambling to clinch a deal to form a government before the June 17th start of the Muslim holy month of Ramadan.
The talks in the Moroccan resort town of Skhirat "will discuss a new draft" agreement for a political agreement to end the conflict, his mission to Libya said on Friday.
It forecast the coming round would be "decisive", a view echoed by top diplomats from Algeria, Egypt and Italy at a meeting hosted by Cairo on Sunday.
"The three countries back" efforts by Leon for a political settlement, Egyptian Foreign Minister Sameh Shoukri told reporters after the meeting.
His Italian counterpart Paolo Gentiloni said the meeting in Morocco "comes at a very important juncture".
He said an accord would also help stem the flow of migration to Europe from Africa via Libya - where people smugglers have taken advantage of the chaos to step up their lucrative business.
Abdelkader Messaleh, a top Algerian foreign ministry official, said Cairo, Rome and Algiers were united in their support for the UN mediation.