Italy will also send teams to help firefighters try to tackle the blaze, which was sparked during fighting Sunday night between Libyan militias and has been raging ever since, a government statement said.
The fire erupted when a rocket struck a tank containing more than six million litres (1.6 million gallons) of fuel before spreading to a second storage site in what the government called a "very dangerous" development.
The authorities feared the blaze could spread still further to a natural gas reservoir, where 90 million litres are stored.
On Monday, the government appealed to several countries for help and Italy, as well as Greece, said aid would be contingent on a halt in the fighting.
In its statement Tuesday, the government again called for a ceasefire.
Combat raged overnight, with a number of explosions heard, but the situation was relatively calm on Tuesday morning.
On Monday, a spokesman for the National Oil Company said the situation was "out of control", and the government urged residents living within a three kilometre radius of the fire to leave their homes.
The depots are located 10 kilometres (six miles) from the city on the road to the international airport, which rival militias have been fiercely fighting for since mid-July.
Firefighters had been battling to extinguish the blaze, but ongoing clashes repeatedly forced them to flee the area. Fighting in the area has claimed the lives of 97 people and left more than 400 injured, the latest health ministry figures show.
On Monday, top world leaders urged an immediate ceasefire and called on the UN "to play an essential role in facilitating the political process" to restore stability to Libya.
While the oil burns, motorists in Tripoli are suffering severe petrol shortages, as service stations have closed over fears for the safety of staff in light of the fighting.
As lawlessness spreads, several countries have warned their citizens not to travel to Libya, while others have advised their citizens to leave the country immediately.
The Tripoli clashes, the most violent since a 2011 revolt that overthrew dictator Moamer Kadhafi, started with a July 13 assault on the airport by armed groups, mainly Islamists.
The attackers are battling to flush out fellow former rebels from the hill town of Zintan, southwest of Tripoli, who have controlled the airport for three years.
Violence has also hit the eastern city of Benghazi, cradle of the revolution, where weekend fighting between the army and Islamists killed 28 people, mostly soldiers.