Euronews has reached out to the French Foreign Affairs Ministry.
In recent months, however, the Trump administration seems to be warming to General Haftar and his LNA although the USA has officially backed the GNA throughout the conflict, the New York Times (NYT) alleged citing anonymous foreign diplomats early this month.
"Behind the scenes there's no doubt about the fact they've supported the (Libyan National Army) with all kinds of equipment, people, training and the like and they've supported Haftar, who has moved now from the east to the west and essentially has taking a lot of real estate to get into a good position for leverage for diplomatic talks", Waldhauser told the House Armed Services Committee.
Asked whether that included ruling the whole country, the official said, "That is up to the people of Libya". The Libyan National Army claimed it had the seized the worldwide airport near Tripoli, which has not been in use for several months now.
Mr Trump's call suggests he endorses Gen Haftar, unlike some of his allies.
Citing Libyan and French officials, several media reports claim Paris supports Haftar with weaponry, training, intelligence and special forces assistance.
The fighting on the outskirts of the city has killed at least 213 people and wounded more than 1,000 people, the World Health Organisation said on Friday.
Over the weekend the LNA dispatched units to the eastern oil ports of Ras Lanuf and Es Sider in case of any attack on them by forces aligned with the Tripoli-based government.
According to the special envoy, the political process in Libya has not seen any progress yet and the potential of violence escalation increases with the influx of arms.
Haftar's LNA is meeting firm resistance in Tripoli.
The Trump administration has met with both Haftar and Serraj in recent years but has provided more support to the GNA.
Foreign powers are anxious but unable to present a united front over the latest flare-up in the cycle of anarchy and warfare that has gripped Libya since dictator Muammar Gaddafi was toppled in 2011.