The statement was published jointly by the foreign ministers of Algeria, Britain, France, Germany, Italy, Morocco, Qatar, Spain, Tunisia, Turkey, the United Arab Emirates and the United States as well as the EU foreign policy chief.
They "call on all parties in the Libyan political dialogue to immediately adopt the political agreement negotiated by the Special Representative to the United Nations, Mr (Bernardino) Leon," it reads.
Libya has had two administrations since August 2014, when a militia alliance that includes Islamists overran the capital, forcing the internationally recognised government to take refuge in Tobruk in the east.
UN envoy Leon has put forward proposals for a power-sharing government, but both the internationally recognised parliament and the Islamist-backed assembly have balked at the appointments.
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The UN Security Council has threatened to impose sanctions on those who block a peace deal in Libya or undermine any political transition in the country, which descended into chaos after the fall of Moamer Kadhafi in 2011.
The new UN-backed government 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.
A meeting hosted by the UN Support Mission in Libya and Britain brought together representatives of 40 countries on Monday to seek ways to support a "Government of National Accord" in Libya.
"There is no other way except, God forbids, a further slide into bloodshed and chaos," said Ali Al-Za'tari, deputy special representative of the secretary-general for Libya in a statement.
A unity government in Libya is seen as the best chance to tackle migrant-smuggling from Libyan territory across the Mediterranean and the rise of the Islamic State group.