The attack in Kunduz occured after a US fighter jet, which had been called in by German troops, blew up two fuel trucks that Nato said at the time had been hijacked by Taliban fighters.
The Afghan government said 99 people were killed in the incident, including 30 civilians, while independent rights groups estimate that between 60 and 70 civilians were killed.
The airstrike sparked outrage in Afghanistan and was publicly condemned by Hamid Karzai, the Afghan president, helping to turn many Germans angered by the incident against the war.
Germany's Bild newspaper reported last month that videos and a secret military report had clearly pointed to civilian casualties at the time when the government and military was denying civilians had been killed.
Franz Josef Jung, who was Germany's defence minister when the attack took place, has since stepped down because of the incident and Karl-Theodor zu Guttenberg, the current defence minister, is also facing calls to resign.
Popal said: "In Kunduz, a large number of young people have lost fathers and whole families. There are a large number of widows now.
"It is the responsibility of the German government to help them."
German courts, according to the lawyer, are prepared to work with him and his team in order to avoid the case going to trial, but Popal said the government's latest offer of compensation was inadequate.
"They suggested $4.36m, but we have not accepted this because this is not just a matter of money, but about the livelihoods of these people and the rest of their lives," he said.
Popal said a team of six lawyers, including two women, went to Kunduz for a month and a half after the airstrike to carry out research, interview residents and victims and gather information about those who lost relatives.
"We have come to the conclusion, after the work that we did, that 137 were killed who were not Taliban," Popal said.
According to Popal's findings, 56 children were among those killed and the number of Taliban fighters killed could have been as few as five or six.
|Two fuel trucks were blown up in the Nato airstrike [EPA]
"But even if they killed 10 Taliban or more, that does not justify killing 137 people," he said.
Popal said he was looking into similar cases in Afghanistan where civilians had been killed in Nato-led air strikes but would not disclose which incidents he was looking to work on.
The lawyer said he wanted Germany to take an active role in developing the district of Char Dara, where the air strike took place, by building schools, clinics and houses and helping women who were widowed to live independent lives so that they could look after their families properly.
"For these women houses must be built. She has to be able to live the life of the man that has been killed, to be able to make a living," Popal said.