Since early April, Haftar, commander of forces loyal to a rival government in eastern Libya, has been launching a campaign to capture Tripoli, where a UN-recognized Government of National Accord (GNA) is headquartered.
Earlier the White House said Trump had discussed "ongoing counterterrorism efforts" by Khalifa Haftar's forces during a telephone call with the Libyan commander on Monday.
It also comes a day after United Nations envoy Ghassan Salame warned of "a widening conflagration" in other parts of the North African country.
Gen. Haftar's troops are advancing from various directions on the outskirts of the city and say they have seized Tripoli's global airport.
This has raised fears of a full-blown civil war in the oil-rich country, which has been mired in chaos since the NATO-backed toppling of long-time ruler Muammar Gaddafi in 2011.
Members of the Libyan internationally recognised government forces are seen at Khallat Farjan area in Tripoli, Libya April 20, 2019.
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More than 200 people have lost their lives and 913 have been wounded ever since clashes erupted in the region as renegade General Khalifa Haftar's Libyan National Army advanced towards Tripoli.
"We are surprised by France's conduct in the face of the Tripoli attack", read a sign held up by the demonstrators.
Libya is split between rival governments in the east and west. President Donald Trump phoned Hifter earlier this week, expressing U.S. support for the leader's perceived stance against terrorism.
News of Trump's phone call "clarifies" the United States position, noted another diplomat, after Britain fought in vain for five days to try to pass a resolution calling for a ceasefire and unconditional humanitarian access to the combat zones. Libya is split between rival governments in the east and west. Moscow said it objected to the British-drafted resolution blaming Haftar for the latest flare-up in violence, and the United States did not give a reason for its decision.
Government forces announced the launch of a "new phase" in the battle for Tripoli with a counter-offensive against Haftar forces.
French Foreign Minister Jean-Yves Le Drian spoke with Pompeo about Libya on Thursday and both agreed on the need for a "rapid" ceasefire and return to the UN-led political process, the French foreign ministry said in a statement.