According to reports, the air strike is the closest yet to an oil and gas facility located nearby since the beginning of the offensive.
Last week the European Union had called on the LNA to stop its attacks, having agreed on a statement after France and Italy sparred over how to handle the conflict.
The attack comes after Libyan parliament head Aguila Saleh Issa told Sputnik that Libya had notified the UN Security Council that Field Marshal Khalifa Haftar's troops, in their offensive on Tripoli, would not attack the country's civilian population.
"Displacements from areas affected by the clashes in an around Tripoli continue to surge", United Nations spokesperson Rheal Leblanc told reporters in Geneva.
As the sound of fighting echoed round their city, residents sought to buy supplies.
Forces loyal to al-Serraj's government have so far kept the eastern offensive at bay. Fierce fighting has broken out around a disused former airport about 11 km (7 miles) from the center.
A war plane belonging to the eastern Libyan forces on Friday blasted a military camp of a force allied to the UN-backed government near the western town of Zuwara, an eastern military source and residents said.
But Serraj's national accord government has managed to halt the advance for now, aided by forces with machine-guns on pickups and steel containers across the road into Tripoli.
After a week of fighting, 75 people have been killed and 323 wounded, including seven civilians killed and 10 wounded, Dr. Syed Jaffar Hussain, WHO representative in Libya, told a Geneva news briefing by telephone from Tripoli.
His forces swept from their eastern stronghold through Libya's sparsely populated desert, taking parts of the south, before beginning their assault on Tripoli. It has been postponed.
As well as the humanitarian cost, the conflict threatens to disrupt oil supplies, increase migration across the Mediterranean to Europe, scupper a United Nations peace plan, and allow Islamist militants to exploit the chaos.