Amid warnings that chaos in Libya has allowed the Islamic State group to make inroads on Europe's doorstep, United Nations envoy Bernardino Leon is pushing for an agreement before the start of the Muslim holy month of Ramadan on June 17.
"The timing for fighting has passed, the moment for bold political decisions has come," G7 leaders said in a closing statement after a summit in Germany.
"Libyan leaders must now grasp the opportunity to conclude these negotiations and form a Government of National Accord accountable to the Libyan people."
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.
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Three previous rounds of peace negotiations between Libya's rival parliaments and governments have failed to reach an accord.
The talks in the Moroccan seaside resort town of Skhirat "will discuss a new draft" of a political agreement to end the conflict, the UN mission to Libya said on Friday.