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Libya's rival parliaments will sign a UN-sponsored agreement next week on forming a national unity government, they announced on Friday, as world leaders press them to end chaos in the country.

Salah el-Makhzoum, a vice president of the Tripoli-based parliament, called this a "happy day" in announcing the accord will be signed December 16.

An official of the internationally recognised parliament, Mohammed Choueib, said that "after lengthy efforts... we announce to our people that we have decided to move beyond this difficult period... and ask everyone to join us".

Choueib said the deal could be signed in Morocco, which hosted most of a year of talks brokered by UN envoy Bernardino Leon that led to the proposed deal in October.

But neither he nor Makhzoum said whether they would have to clear the signing with their respective legislative bodies, which had rejected the deal after their negotiating teams agreed to it in October.

And just Sunday, delegates from both sides announced they had reached a joint "declaration of principles" aimed at resolving a crisis after secret talks that did not include the UN.

Under the UN-brokered deal, Libya would be governed by a nine-member presidential council comprising a prime minister, five deputy premiers and three senior ministers.

Libya descended into chaos following the 2011 overthrow and killing of long-time dictator Muammar Gaddafi.

The oil-rich country has had rival administrations since August 2014, when an Islamist-backed militia alliance overran Tripoli, forcing the recognised government to take refuge in the east.

Protesters reject UN deal

Hundreds of protesters gathered in Tripoli's main square on Friday afternoon, waving Libyan flags and holding signs calling for a rejection of the UN deal and backing the one reached at the weekend.

They were called onto the streets by Libya Dawn, the Islamist militia coalition that is a key backer of the Tripoli government.

Demonstrator Abdel Hamid Zawawi said: "After I saw that the EU countries and the US are insisting on the UN deal, I was convinced (it) should be out of the question."

After I saw that the EU countries and the US are insisting on the UN deal, I was convinced (it) should be out of the question - Libyan protester

On Tuesday, after the announcement of the separate agreement, ambassadors to Libya from several EU countries and the United States warned against attempts to derail the UN-brokered deal, saying it was the only way forward.

Friday's announcement came just two days before world leaders are set to gather in Rome to try to speed up the formation of a unity government in Libya, where chaos is fuelling the rise of the Islamic State group (IS).

It was not immediately clear how Friday's development might affect that meeting or its agenda.

Italy's Foreign Minister Paolo Gentiloni, due to co-chair the talks with US counterpart John Kerry, has said the aim is a "decisive push" for a deal to help create stability, ease a dire humanitarian situation and smother a flourishing jihadist hotbed.

Kerry and Gentiloni will sit down with Russian Foreign Minister Sergei Lavrov and representatives from Britain, China and France, Germany, Spain as well as Algeria, Chad, Morocco, Niger, Qatar, Tunisia, Turkey and the United Arab Emirates.

"You can never repeat often enough the danger that the presence of Daesh represents for Libya," Tunisian PM Habib Essid said Friday on the sidelines of a Mediterranean security conference in Rome, using an Arabic acronym for IS.

Friday's announcement came on a second day of meetings in Tunis with Leon's successor, Martin Kobler.

UN envoy 'very encouraged'

Kobler said on Thursday that he felt "very encouraged" and had "big confidence in our meeting tomorrow (Friday) because we are going to define the messages for the meeting in Rome".

There must be a legitimate government very soon -UN envoy to Libya Martin Kobler

"The international community is very interested in this process, in particular the threat emanating from terrorism," he said.

"There must be a legitimate government very soon."

The UN estimates there are between 2,000 and 3,000 jihadist fighters in Libya, and local officials warn of hundreds of Tunisians, Sudanese or Nigerians travelling there for training.

It was not yet clear who would represent the rival factions in Rome.

European sources say the aim is to form a unity government by the end of the year, after which UN sanctions could be imposed to force an accord.

"There is an absolute emergency. Every week that passes is used by IS to try to make Libya a terrorist base," French European Affairs Minister Harlem Desir said on Friday.

Italy's Prime Minister Matteo Renzi has been saying for months that the Islamist threat is as severe in Libya as in Syria, and that Rome is ready to take command of a military mission should the UN agree.