World leaders and the United Nations urged Libya's warring parties Friday to sign a proposed peace deal installing a national unity government, after a cool response from some lawmakers in the country's rival parliaments.

Libya has had two administrations since August last year when a militia alliance that includes Islamists overran the capital, forcing the internationally recognised government to take refuge in the east.

The new government proposed by UN envoy Bernardino Leon would be headed by Fayez el-Sarraj, a deputy in the Tripoli parliament, and include three deputy prime ministers, one each from the west, east and south of the country.

"There is no more time to waste," said a joint statement released by the governments of Britain, France, Germany, Italy, Spain and the United States.

"Delays in forming a unity government will only prolong the suffering of the Libyan people and benefit terrorists seeking to take advantage of the chaos."

The UN Security Council also unanimously called on all stakeholders in the country to support the deal and reiterated it was "prepared to sanction those who threaten Libya's peace, stability and security or that undermine the successful completion of its political transition."

The country descended into chaos after the fall of Moamer Kadhafi in 2011, with the two sides vying for power as well as several groups battling for control of its vast resource wealth.

Sarraj, a graduate in business management, has been involved in dialogue that tried to bring together the various actors of Libyan society to end the crisis.

"After a year of work in this process, after working with more than 150 Libyan personalities from all the regions... finally the moment has come in which we can propose a national unity government," UN envoy Leon told a news conference in Morocco.

- 'A significant milestone' -

UN chief Ban Ki-moon welcomed the news, and appealed to warring factions to sign the accord.

He urged Libya's leaders "not to squander this opportunity to put the country back on the path to building a state that reflects the spirit and ambitions of the 2011 revolution.

"Now is the time for the parties to the political dialogue to endorse this proposal and sign the agreement without delay."

US Secretary of State John Kerry called the proposed accord a "significant milestone in the Libyan political process" and said the US "stands ready" to support the unity government.

Previous deals to ensure a ceasefire and restore stability to the strife-torn country have fallen apart, and officials from both sides expressed scepticism after the announcement.

- Turn Libya into 'joke' -

Abdulsalam Bilashahir, from the rival Tripoli-based General National Congress, told the BBC: "We are not a part of this (proposed) government. It means nothing to us and we were not consulted."

Ibrahim Alzaghiat, from the internationally recognised House of Representatives based in Tobruk, was also quoted as saying: "This proposed government will lead to the division of Libya and will turn it into a joke. Mr Leon's choice was unwise."

But Leon said the new government list could be agreed by all sides.

"Too many Libyans have lost their lives, too many children have been suffering, too many mothers have been suffering... around 2.4 million Libyans are in a situation of humanitarian need," he said..

"This was not an easy task. We have been listening to many people, inside and outside the dialogue. And we believe that this list can work.

"It is a quite reasonably good list of names, politicians, personalities that will do their best, I'm sure, to take their country out of this crisis," he said.

Years of chaos in Libya have turned it into a hub for human-trafficking gangs, which have fuelled Europe's huge migrant crisis by sending thousands of people on the perilous journey across the Mediterranean.

More than 3,000 people have died or are feared drowned after trying to make the crossing since the start of this year, according to the UN refugee agency.

On Thursday, Libyan authorities said they had arrested some 300 migrants as they were preparing to board boats.

EU foreign policy chief Federica Mogherini welcomed the announcement from Libya, and pledged some 100 million euros ($110 million) in support for the new government.

"There is no time to waste in the formation of a government of national accord, so that it may -- with the full recognition and support of the international community -- begin working for the benefit of all the Libyan people," she said in a statement.