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 Tuesday 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.
Ghattas did not elaborate on who the negotiating teams would meet in Berlin.
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.
It said it would "provide significant support" to help a new government rebuild infrastructure, including restoring public services and strengthening the economy.
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.
The 69-article plan provides for the formation of a transitional Government of National Unity for a period of one year, renewable once.
It stipulates that the parliament elected in June last year, most of whose members back the internationally recognised government in Tobruk, should be the legislative authority for the interim period.
But it also provides for the formation of a High Council of State, mostly formed of members of the rival parliament in Tripoli, which "shall express binding opinion with a qualified majority on draft laws."
The two sides would commit themselves to the integration of their opposing militias into a reformed military under direct government control with former rebel fighters offered the opportunity join up or be reintegrated into civilian life.
The agreement sets out interim security arrangements for the withdrawal of armed formations from towns and cities and a timetable for disarming.
"The Government of National Accord through its different relevant institutions, including the army and police, shall take the necessary steps to combat terrorist threats in Libya," the draft says.
Both Libyan administrations have been engaged in fighting with loyalists of the Islamic State group, which has taken several coastal towns to the alarm of an international community fearful of a jihadist foothold on Europe's doorstep.
IS, which controls swathes of Syria and Iraq, has won the loyalty of several Islamist groups in Libya and claimed responsibility for a series of attacks and atrocities, including the killings of dozens of Egyptian and Ethiopian Christians.