The Islamist-backed Fajr Libya militia alliance seized Tripoli in August and installed a government and a parliament opposed to the elected legislature and the country's internationally-recognized government, both of which have taken refuge in the country's far east.
Talks are due to resume on today in Algiers and focus on the formation of a government of national unity as well as security issues.
"We strongly urge all participants to the dialogue to negotiate in good faith and use this opportunity to finalize agreements on the formation of a national unity government and make arrangements for an unconditional ceasefire," a US-European joint statement read.
"Only through compromise can Libya move toward a more secure, stable, and prosperous future." The statement was issued by Foreign Ministers Laurent Fabius of France, Frank-Walter Steinmeier of Germany, Paolo Gentiloni of Italy and Jose Manuel Garcia-Margallo of Spain, along with British Foreign Secretary Philip Hammond and US Secretary of State John Kerry.
"We call for the immediate cessation of airstrikes and ground offensives," they wrote, urging the warring factions to halt the fighting and engage in political dialogue without delay.
"Such provocations undermine the UN talks and threaten chances for reconciliation." The top diplomats warned the UN could slap sanctions on parties seen as threatening Libyan peace, stability or security. "The growing threat of terrorism in Libya is of grave concern to the international community," they wrote.
"Extremists use the lack of order to their advantage, causing further suffering and bloodshed both inside and outside Libya." The diplomats vowed global support for an eventual unity government in helping Libya address its challenges.
Libya has been gripped by chaos and violence since its 2011 revolution that toppled veteran dictator Moamer Kadhafi, with rival factions battling for control of its cities and oil wealth.