NATO initially said it believed the casualties were all Taliban fighters, but later acknowledged that large numbers of civilians were being treated in hospitals in the area, according to Reuters.
President Hamid Karzai's office gave a death toll of 90 and said an investigation team had gone to the scene.
"No civilians must be harmed during military operations," Karzai said in a statement. "Targeting civilians under no circumstances is acceptable."
Kunduz Gov. Mohammad Omar told the Associated Press 90 people were killed. A senior Afghan police officer, speaking on condition of anonymity, said that included about 40 civilians who were siphoning fuel from the trucks.
Mohammad Sarwar, a tribal elder in the province, told the AP that Taliban fighters had hijacked the tankers and were offering fuel to a crowd of villagers when the tankers were bombed.
"We blame both the Taliban and the government," Sarwar said.
The airstrike is likely to intensify concern over civilian casualties in the Afghan war and U.S. strategy in the months ahead. Top NATO commander, Gen. Stanley McChrystal, has ordered curbs on airstrikes amid concerns among Afghans over civilians killed in military operations.
On Thursday, Pentagon leaders sought to shore up support for the U.S. military effort in Afghanistan. They said the new strategy needs more time, and they left the door open to asking for more troops.
"I don't believe that the war is slipping through the administration's fingers," Gates said at a Pentagon news conference. "The nation has been at war for eight years. The fact that Americans would be tired of having their sons and daughters at risk and in battle is not surprising."
Regarding Friday's airstrike, Lieutenant-Commander Christine Sidenstricker, press officer for the U.S. and NATO-led International Security Assistance Force, told news agencies that Afghan authorities had reported two fuel trucks hijacked. NATO aircraft spotted them on a river bank.
"The strike was against insurgents. That's who we believe were killed. But we are absolutely investigating" reports of civilian deaths, she said.
The strike took place near the border with Tajikistan, in a part of the country once seen as relatively secure but where Taliban attacks have become increasingly frequent. The Taliban consider fuel shipments a strategic target because military forces rely upon them.
The Kunduz area is patrolled mainly by NATO's German contingent. Germany confirmed its commander in the area gave approval for the aircraft to open fire.
A Defense Ministry spokesman in Berlin told Reuters it believed more than 50 fighters were killed and had no information about deaths of civilians.
British Foreign Secretary David Miliband called for a "prompt and urgent investigation".
"It is a vital time for NATO and Afghanistan's people to come together," he told SKY news. "We have a very strong NATO commitment. We need a strong Afghan commitment and obviously incidents like this can only undermine that."
---- Compiled from wire reports and other media sources