There were reports of a fast amphibious craft being used in the operation.
India's External Affairs Minister Sushma Swaraj said the country's full contingent of 15 Central Reserve Police Force peacekeepers had been evacuated from Tripoli because the situation in Libya had "suddenly worsened".
The Italian multinational oil and gas company Eni decided to evacuate all its Italian personnel from the country.
The UN is also due to pull out non-essential staff.
Residents of Tripoli have reportedly begun stocking up on food and fuel. But BBC Arab affairs editor Sebastian Usher says many of those near the fighting are remaining in their homes for now, for fear of looting should they leave.
Some fear a long operation such as that which Gen Haftar mounted to take the eastern city of Benghazi from Islamist fighters in 2017.
Who are the opposing forces?
Libya has been wracked by unrest since the overthrow of Gaddafi. Dozens of militias operate in the country.
Recently they have been allying either with the UN-backed GNA, based in Tripoli, or the LNA of Gen Haftar, a tough anti-Islamist who has the support of Egypt and the UAE and is strong in eastern Libya.
Gen Haftar helped Gaddafi seize power in 1969 before falling out with him and going into exile in the US. He returned in 2011 after the uprising against Gaddafi began and became a rebel commander.
The unity government was created at talks in 2015 but has struggled to assert national control.
Prime Minister Fayez al-Serraj said on Saturday he would defend the capital.
Mr Serraj said he had offered concessions to Gen Haftar to avoid bloodshed, only to be "stabbed in the back".
Back to square one?
Analysis by Rana Jawad, BBC North Africa correspondent, in Tunis
The rogue general's defiance suggests that, despite international condemnation of his recent moves, he believes he can only secure a place in Libya's future political makeup through military means.
Diplomats are worried because the manner and timing of the attack mean he is unlikely to back down unless he is defeated.
Few thought he would go ahead and launch this operation - which he has long threatened to do - because they believed ongoing talks that saw him go from Paris to Palermo and the UAE for more than a year would buy time until a new political settlement was reached through negotiations and an eventual electoral process.
Today, Western nations have few cards to play to de-escalate the violence and once again find themselves in a position where they may need to start from scratch.