It was unclear whether there had been any casualties in the incident which happened late on Friday.
Firefighters spent all night tackling the blaze, but fires were still burning on Saturday morning.
The tankers were reportedly transporting fuel for Nato forces and were parked at the time of the attack.
An Afghan security official quoted by the AP news agency said that at least 400 fuel tankers caught fire in a parking lot in the outskirts of Kabul.
Hashmat Stanikzai, spokesman for Kabul’s police chief, said that police were investigating the cause of the fire.
In a statement, Taliban spokesman Zabihullah Mujahid said it had targeted foreign forces’ fuel tanker supplies, AP reports.
While attacks on Nato tankers have been commonplace in Pakistan in recent years, correspondents say they have been less frequent in Afghanistan.
On Wednesday a Taliban suicide bomber killed at least eight military officers in an attack on an air force bus in Kabul,
Afghans are still awaiting the results of a run-off vote held in mid-June to find a successor to President Hamid Karzai.
Afghanistan’s election commission has delayed the release of preliminary results until next week amid allegations of “extraordinary” levels of fraud.
Nearly a million votes are being re-counted and both candidates – former foreign minister Abdullah Abdullah and ex-finance minister Ashraf Ghani – have said fraud has taken place.
Source: BBC news
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