Gulam Mohyuddin, the local chief of police, said on Friday that the air raid had hit the tankers in Kunduz province, near the Tajikistan border.
James Bays, Al Jazeera's correspondent in Kabul, said members of the Taliban had hijacked the lorries, travelling from Tajikistan, and taken them to the district of Aliabad.
"The Taliban there said 'help yourself' to the village, and a large crowd appeared," Bays said.
"It appears that then the US launched a bombing mission to bomb those trucks."
Jon Stock, press officer for Nato's International Security Assistance Force (Isaf), said: "I can confirm that there was an air strike last night or early this morning."
"Isaf's target in the air raid was insurgents," he said.
Mohammad Omar, the Kunduz governor, said that many Taliban fighters were killed in the attack, including a senior Taliban commander.
Zabihullah Mujahid, a Taliban spokesman, said that as many as 90 civilians, who had come out to take the fuel from the lorries, had been killed in the attack.
He confirmed that the two lorries had been hijacked, but said that only one was hit in the air raid after the other got stuck in the mud in Aliabad district and was abandoned.
An Al Jazeera producer in Kunduz province said that he had seen at least 50 injured people in a local hospital, all burn-victims, and all of them said they had lost family in the incident.
"My brother was burnt when the aircraft bombed the fuel tankers. I don't know whether he is dead or alive," one villager said outside the hospital.
Our correspondent said: "If these reports are confirmed, this will be a definite blow to General [Stanley] McChrystal, the US and Nato army commander in Afghanistan, who has urged US forces to avoid civilian causalities where at all possible."
Source: Al Jazeera (English)