The G7 later responded to the fighting with a statement urging an end to military operations.
"We strongly oppose any military action in Libya," the statement read, reiterating their support for UN-led efforts to bring elections and calling on all countries to support the "sustainable stabilisation of Libya".
The UN Security Council held a close-door meeting late on Friday. Afterwards the German UN ambassador Christoph Heusgen said members had "called on LNA forces to halt all military movements".
"There can be no military solution to the conflict," he said.
A Russian spokesman earlier told reporters the Kremlin does not support Gen Haftar's advance and said it wants a solution by "peaceful political means".
A conference was planned in Libya later this month for talks over ending the country's long-running crisis.
Hope dashed for a political resolution?
By Sebastian Usher, BBC Arab affairs editor
Khalifa Haftar's forces have met with mixed fortunes.
To the south, they appear to have got close to the outskirts of the capital, at one point claiming to have taken the airport. But to the west, they appear to have been pushed back.
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.
He returned during the revolution and he's subsequently become the most powerful military leader in a country rife with militias, allied to a rival government in the east.
Despite the chorus of international concern over his actions, he has had support from powerful outside players, including the UAE and Egypt.
Efforts towards a political resolution for Libya have foundered time after time. The most recent hopes may once again have been dashed.
Who is Khalifa Haftar?
A former army officer, he helped Colonel Muammar 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.
In December Haftar met Prime Minister Fayez al-Serraj from the UN-backed government at a conference but refused to attend official talks.
He visited Saudi Arabia last week, where he met King Salman and Crown Prince Mohammed bin Salman for talks.