The announcement of the air raid was made on the Facebook page of the "media office" of Haftar's self-styled Libyan National Army (LNA) as fighting raged around 50km south of Tripoli. "We have formed an operative staff including units of the armed forces and the interior ministry".
He did not provide details on the number of USA troops that have been withdrawn or on how many remain inside the country.
It's still unclear how much this is a show of force to bolster Gen Haftar's position or a genuine effort to seize Tripoli. Libya will always be a civilian state and the army will protect it and secure the people.' he said.
The internationally-recognised unity government, born out of UN-backed talks, has struggled to assert its control.
Haftar, 75, who casts himself as a foe of Islamist extremism but is viewed by opponents as a new dictator in the mould of Gaddafi, enjoys the backing of Egypt and the United Arab Emirates, which see him as a bulwark against Islamists and have supported him militarily.
The evacuation came as Field Marshal Haftar's offensive entered its fourth day, with units of his Libyan National Army fighting Tripoli militias in the city's southern suburbs.
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At least one armed group from Misrata known as Brigade 166 arrived Saturday in eastern Tripoli with dozens of vehicles, some mounted with anti-aircraft guns, to join the counter-offensive, an AFP photographer said.
Video has now emerged showing U.S. Navy Landing Craft Air Cushion (LCAC) hovercraft approaching and landing on the beach in the town of Janzour, which is located just a few miles to the west of Tripoli.
The rival militias, which are affiliated with a United Nations -backed government in Tripoli, said they had also carried out airstrikes, slowing Hifter's advance.
Fayez Sarraj, chairman of the Presidential Council of Libya, said his government had offered concessions to Hifter "to avoid bloodshed and to end divisions" and was surprised by Hifter's order to take the capital.
"To date, Haftar´s operation has mostly failed to go according to plan, and it has now galvanised western Libyan forces against him", said analyst Wolfram Lacher.
German Foreign Minister Heiko Maas said there should be pressure on all the actors in Libya "especially general Haftar". Resulting from years-long civil conflict, Libya has no single government now, with LNA backing the Tobruk-based parliament which governs the East of Libya, and the GNA which controls Libya's western parts from Tripoli, reports Sputnik.
"We are determined" to hold the talks "as scheduled" unless prevented by serious obstacles, Salame told a press conference.