Witnesses said shortly after the attack a US aircraft had bombed the oil tankers as local villagers were trying to collect free fuel on the invitation of the Taliban fighters.
The tankers had been seized by Taliban fighters as they were travelling from Tajikistan to Kabul.
Bomb attack feared
A German commander called in the air raid fearing that the tankers would be used in an attack on their base just six kilometres away, Germany's defence minister has said.
The air raid provoked criticism from Karzai, who called it "a major error of judgement", and the European Union, which said it harmed efforts at nation-building in Afghanistan.
Speaking to the Reuters news agency on Sunday, Mohammadullah Baktash, another of the investigators, said: "We cannot say whether the air strike was neccessary or not.
"We will present our report to Karzai and it will be up to him to investigate with the Germans."
The commander of US and Nato forces in Afghanistan promised a "complete investigation" into the bombing, saying "nothing is more important than the safety and protection of the Afghan people".
It has not yet released details of the inquiry.