UN envoy Bernardino Leon presented a draft peace agreement to delegations from the North African nation's rival parliaments at talks in Morocco late on Monday.
With strong support from world leaders, Leon is pushing for a final accord before the start of the Muslim holy month of Ramadan on June 17.
Leon spent this morning shuttling between the rival negotiating teams to gauge their response.
"Then we will all head to Berlin to meet European leaders and member countries of the UN Security Council," UN mission spokesman Samir Ghattas told AFP.
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But Morocco's official MAP news agency said that the talks would be joined by the top diplomats of the five Security Council permanent members -- Britain, China, France, Russia and the United States.
G7 leaders have thrown their support behind Leon's efforts to persuade the factions to forge a united administration to replace the rival governments in the capital Tripoli and the eastern town of Tobruk.
In a closing statement after a summit in Germany, the G7 called on Libyan leaders to take "bold political decisions" to end four-year of devastating conflict.
Libya descended into chaos after a 2011 NATO-backed uprising toppled and killed veteran dictator Moamer Kadhafi, with heavily armed former rebels carving out fiefdoms across the country.
Jihadist groups have exploited the lawlessness, which has also prompted a huge influx of migrants trying to make the dangerous crossing to Europe, with shipwrecks leaving hundreds dead and the European Union straining to respond.
The latest draft agreement put forward by the UN mission is the fourth. Three previous rounds of negotiations between Libya's rival parliaments and governments failed to reach an accord.