Libya's interim government said in a statement posted that the fire could trigger a "humanitarian and environmental disaster" in Tripoli, appealing for "international help" to extinguish the inferno.
It did not say what it specifically needed.
The blaze had spread to a second depot by Monday afternoon, the government said. It was unclear if there were any injuries from the fire.
Libyan television stations called on residents to evacuate areas within a 5-kilometre radius of the airport. Many Libyan families scrambled to leave. Black smoke billowed over the Tripoli skyline.
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Mohammed al-Harari, the spokesman for the Libyan National Oil Company, said the oil depot had a capacity of 6 million litres and that if the fire was not brought under control, it could ignite liquid gas nearby.
Fire trucks from several nearby cities and towns have been deployed to help extinguish the blaze, said a Libyan security official, speaking on condition of anonymity because he is not authorised to talk to journalists.
The Health Ministry said yesterday that the fighting has so far killed 79 people and wounded more than 400.
More than three years after dictator Muammer Gaddafi's downfall, Libya is witnessing one of the worst bouts of violence amid growing lawlessness in the country.