The LNA says it has 85,000 men, but this includes soldiers paid by the central government that it hopes to inherit.
A US amphibious hovercraft departs with evacuees from Janzur, west of Tripoli, Libya, Sunday, April 7, 2019.
Haftar last week ordered his self-styled Libyan National Army (LNA), which is allied to a parallel administration in the east, to march on Tripoli, the seat of the internationally recognised Government of National Accord (GNA) which is protected by an array of militias.
The UN Humanitarian Coordinator in Libya, Maria Ribeiro, said Monday the fighting had displaced more than 2,800 people, blocked rescuers from reaching casualties and damaged electricity lines.
Late last week, Haftar announced the launch of an ambitious campaign to capture Tripoli, where the GNA is headquartered.
Matiga airport, in an eastern suburb, was bombed and closed, authorities said.
Haftar's Libyan National Army (LNA) forces have been advancing on Tripoli for several days, vowing to eliminate "terrorists and extremists" there.
But the Tripoli government of Prime Minister Fayez al-Serraj, which reported 11 deaths without specifying on which side, had armed groups arriving from nearby Misrata to block the LNA.
At least 35 people have been killed since 4 April, the date of the start of Haftar forces' attack on the Libyan capital, according to new data issued by the Government of National Accord, amid increasing worldwide calls to stop the attack.
Mr Serraj has run Tripoli since 2016 as part of a UN-brokered deal boycotted by Mr Haftar.
United Nations special envoy to Libya Ghassan Salame condemned the attack on Tripoli's only functioning airport, saying the United Nations was "deeply concerned for the welfare of the civilian population in the ongoing violence".
The violence has cast doubt on the United Nations plan to hold a conference from 14 to 16 April to arrange for the elections, as a way out of the ongoing chaos since Gaddafi's ousting under Western support eight years ago.
While fighting near the capital continues, a United Nations envoy said he does not see a peace conference taking place as scheduled next week.
The UN, US and European Union and the Group of Seven economic bloc have all called for a ceasefire.
Haftar casts himself as a foe of extremism but is viewed by opponents as a new dictator in the mould of Gaddafi, whose 40 years rule saw torture, disappearances and assassinations.
Its elite force, Saiqa (Lightning), numbers some 3,500, while Haftar's sons also have well-equipped troops, LNA sources say.
France, which has close links to Haftar, said it had no prior warning of his push for Tripoli, a diplomatic source said.
The video emerged as the US temporarily withdrew some of its forces from Libya due to the "increasingly complex and unpredictable" security situation, according to Marine Corps General Thomas Waldhauser, head of US Africa Command.
France's stance has created tensions with Italy, which has sought a leading role to end the turmoil in its former colony.