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.
The quest for a deal seeks to prevent the oil-rich and strategic North African nation from crumbling into a failed state.
Bernardino Leon, chief of the United Nations Support Mission in Libya, presented the draft to delegations from the country's rival sides at talks in Morocco yesterday.
"We have distributed, as you will have seen, a new proposed agreement. All I can tell you for now is that the reaction is positive," Leon told journalists.
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"We are looking at the possibility of a triple consensus -- within Libyan society, among the participants in the dialogue and also the international community."
He said there was "sense of optimism" emerging from the talks, but warned that no agreement would work without the backing of armed groups in Libya.
The Spanish diplomat had spent Tuesday morning shuttling between the 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, without saying whom they would meet.
German Foreign Minister Frank-Walter Steinmeier has invited them to Berlin to continue talks Wednesday with Leon as well as meet diplomats from the UN Security Council's permanent five members, plus Italy, Spain and the European Union, his ministry said.
In a closing statement after a summit in Germany, the G7 called on Libyan leaders to take "bold political decisions" to end four years of devastating conflict.