President Emmanuel Macron reiterated France's support for Libya's beleaguered Government of National Accord (GNA), after talks Wednesday with Prime Minister Fayez al-Sarraj, the French presidency said in a statement.
"In this context, a proposal was made for tracing a ceasefire line, under international supervision," to halt the military advance on Tripoli by Sarraj's strongman rival Khalifa Haftar, the presidency said.
Tensions between Paris and the GNA had flared after Haftar began his offensive five weeks ago and Sarraj accused the French government of tacitly supporting Haftar's campaign.
France has said it views Haftar, who controls large swathes of the country's east where he has helped curtail Islamic terrorist activities, as a key player in rebuilding Libya after years of strife.
In their talks in Paris Wednesday, Macron told Sarraj that there was no military solution to the problem and called for an unconditional ceasefire to end the hostilities between the two factions.
"The two leaders agreed on the importance of extending and deepening the dialogue with all stakeholders in Libya, including in the east, south and west of the country, and with civil society," the presidency statement said.
It did not specify where any ceasefire line might be drawn, now that Haftar's forces have reached the southern outskirts of Tripoli.
After the initial advance, forces loyal to the GNA launched a counter-offensive that has led to a stalemate on the ground.
The fighting has killed at least 430 people and wounded over 2,000 while displacing 55,000 others, according to UN estimates.
Hopes for a halt in the fighting to mark the onset of the Muslim holy month of Ramadan were dashed this week after Haftar urged his troops to inflict "an even harder" lesson on forces loyal to the country's internationally recognised government.
And the GNA has previously rejected any ceasefire unless Haftar pulls his troops back to the areas they held before the April 4 offensive on the capital, in the south and east of the country.