His move is the latest in a cycle of conflict and anarchy since the 2011 toppling of former dictator Muammar Gaddafi.
Analysts believe the campaign on Tripoli could potentially reignite large-scale fighting among the country's rival powers and undermine worldwide efforts to reunite the fractured North African nation.
Fighting in recent days has been taking place on the outskirts of Tripoli as LNA forces have been bogged down by groups aligned with the Government of National Accord (GNA).
"On Sunday, GNA military spokesman Mohammed Ghnounou told Sputnik that forces loyal to the GNA leadership had downed a warplane belonging to Haftar's army".More news: Giuliani: Going to See 'No Collusion' From Mueller Report
It is not clear whether Gen Haftar's surprise march on Tripoli was launched with the prior knowledge or the approval of the Egyptians.
The army, led by General Khalifa Haftar, is allied with the eastern-based government, as the country is politically divided between western and eastern governments. Moreover, militias, mostly Islamist, have held sway over large regions, particularly in the west and south of the country.
More than 120 people have been killed since a Libyan military commander launched an assault on the capital 10 days ago, igniting clashes with rival militias, the United Nations health agency said Sunday.
WHO's Libya Twitter account posted an update of "casualties" and said it was "sending medical supplies, health staff support for first- and second-line responders".
"The World Health Organization strongly condemns repeated attacks on healthcare workers, vehicles and facilities", WHO tweeted'.More news: As Haftar meets Sisi, GNA forces shoot down LNA fighter jet
As well as fighting on the ground, the two sides have launched daily air raids and accuse each other of targeting civilians.
More than 13,500 people had been displaced by the clashes, including 4,000 in the past 24 hours, and more than 900 residents are living in shelters, the U.N. Office for the Coordination of Humanitarian Affairs said Saturday.
United Nations envoy Ghassan Salame said a school was bombed in the town of Ain Zara, around 15 kilometres southeast of Tripoli, without saying who was responsible.
"UNSMIL warns that the bombing of schools, hospitals, ambulances and civilian areas is strictly prohibited by International Humanitarian Law", the Mission said in a statement.More news: Respawn Co-Founder Jason West Has Joined Epic Games