"There is no time to lose for the national unity government to assume its functions and securely establish itself in Tripoli," said Foreign Minister Jean-Marc Ayrault, following a meeting on the sidelines of the Munich Security Conference.
The meeting was attended by US Secretary of State John Kerry and his counterparts from Britain, Egypt, Germany and Italy, as well as EU and UN representatives.
The speaker of Libya's internationally recognized parliament, Aguila Saleh, was also present. His parliament had given itself to Sunday to form a new national unity government aimed at ending years of chaos in the North African country.
"They must move fast, as fast as possible. It is in the interest of the Libyan people, the regional countries and Europe," said Ayrault, who took over as France's foreign minister from Laurent Fabius this week. "Those who oppose the process... will be subject to sanctions. That point is clear."
The Islamic State jihadist group has taken advantage of the turmoil to establish a stronghold in the coastal city of Sirte.
Libya has been in chaos since the 2011 ouster of longtime dictator Muammar Gaddafi, with two rival administrations and armed groups fighting for control of the oil-rich country.
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A militia alliance including Islamists overran Tripoli in August 2014, establishing its own government and parliament and causing the recognized administration to flee to the country's remote east.