Rival governments have battled for power in the North African country since last August and just Wednesday an air strike blamed on the internationally recognised administration hit an air base controlled by its opponent.
Jihadists loyal to the Islamic State group which controls swathes of Iraq and Syria have exploited the power struggle to launch increasingly grisly attacks including the videotaped beheadings of 21 Christians in February.
UN envoy Bernardino Leon, who has been shuttling between the warring sides for months, said that the reported drowning of up to 400 would-be asylum-seekers off the Libyan coast earlier this week should be the spur for an agreement.
"I really hope that the negotiators that are coming today are understanding that we cannot wait any more and this will really be the final round," Leon said.
"This is Libya today -- terrorism, no control on the borders, people dying every day in the Mediterranean, air strikes ... it cannot go on.
"The patience of Libyans is finished, and the patience of the international community is finished."
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The UN envoy called on the rival negotiating teams to thrash out the full details of a unity government, including the names of ministers, to replace the rival administrations in Tripoli and Tobruk.
The internationally recognised government has been based in the eastern town since an Islamist-backed militia alliance seized the capital in August.
Its loyalists have carried out repeated air strikes on Tripoli and third city Misrata while its opponents have attacked the main eastern oil export terminals dealing a heavy blow to Libya's main revenue earner.
Leon slammed the latest air strike on Mitiga airport, east of Tripoli, on Wednesday.
"It is an extremely negative move and of course it is unacceptable," he said.
"We hope that there will be an investigation on who is behind these attacks."
Libya has been wracked by violence ever since the overthrow of longtime dictator Moamer Kadhafi in a NATO-backed uprising in 2011.
The multiple rebel forces that defeated him seized what they could of his regime's vast arsenal of heavy weaponry and set up a myriad of militias that have battled for their share of Libya's vast oil resources ever since.