Libyan officials have called on local residents to leave the area within a perimeter of 5km
A second fuel tank in the Libyan capital Tripoli has caught fire, which Libya's National Oil Company has described as "out of control".
It comes hours after the authorities appealed for international assistance to try to contain the huge blaze.
The government blames clashes between rival militias for igniting the fire, which it says may cause a humanitarian and environmental disaster.
It is the largest facility in Tripoli, containing 90 million litres of fuel.
At least 97 people have been killed in fighting between rival militia groups battling for control of Tripoli's main airport in the past week.
Fighting in the eastern city of Benghazi has also intensified, with at least 38 people killed in clashes between troops loyal to the Libyan government and Islamist fighters on Sunday.
Firefighters almost managed to put out the first fire but had to withdraw after fighting resumed in the area, Libyan oil company spokesman Mohamed Al-Harrai told the BBC.
Fighting between rival militias in Tripoli and Benghazi has intensified in recent weeks
Several people have been injured in shelling near Tripoli airport
He said shrapnel hit a second fuel tank, igniting a new flame, and the fuel compound was still being hit.
They have run out of all options and are no longer in touch with the government, he added.
A statement by the prime minister's office said it had requested international assistance "as a precaution".
Residents within 3-5km (2-3 miles) of the area have been urged to evacuate, amid fears of a massive explosion if tanks are breached.
But evacuations could be difficult, warns the BBC's Rana Jawad in Tripoli, due to the precarious security situation.
The fuel storage site, which belongs to the Brega oil and gas company, is the main hub for distribution of petrol in the city.
It is located on the main airport road, where much of the fighting of the past two weeks between rival militias has been taking place.
Officials have called on rival militias to cease fire in order to allow firefighters to do their job.
Militias controlling large parts of the country are behind Libya's worst violence since the 2011 uprising that toppled Col Muammar Gaddafi.
On Sunday, France and Germany joined the US and UK in advising their nationals in Libya to leave immediately.
It comes after the UN, US and Turkey announced they were withdrawing staff from Libya due to the surge in violence.
Libyan government officials have warned of the possibility of a break-up of the country if clashes over Tripoli airport continue.
Members of the Islamist Libya Revolutionaries Operations Room (LROR) are trying to seize control of the airport, which has been in the hands of the Zintan militia since the overthrow of Col Gaddafi.
The government has been unable to disarm the numerous armed groups that took part in the 2011 uprising and which have divided the country.
In Benghazi, a coalition of forces including the army have been led by a rogue former general Khalifa Haftar for months.
They say they aim to dislodge Islamist militants from the city.