A German tank opened fire on the vehicles only to discover later that Afghan soldiers had been inside them.
"However, Afghan army officials say their troops were in clearly marked military vehicles, and six soldiers were killed, not five as claimed by the Germans," Al Jazeera's James Bays, reporting from Kabul, said.
Muhboballuh Sayedi, the Kunduz provincial government spokesman, said Afghan commanders were meeting with international forces to discuss the incident.
The Afghan defence ministry issued a statement condemning the incident and expressing condolences to families of the dead soldiers.
"The incident is under investigation," General Mohammad Zahir Azimi, the Afghan defence ministry spokesman, told the AFP news agency.
|More German troops are expected to be deployed in Afghanistan [AFP]
The German military also said that it would carry out a thorough investigation.
Germany is the third-largest Nato contributor to the war with some 4,300 troops in Afghanistan, most of them based in northern Kunduz where Taliban attacks and strength have increased over the past year.
Last month a German general said that the Nato force in Afghanistan was planning an offensive against the Taliban in Kunduz later this year.
Bruno Kasdorf, the chief of staff at the International Security Assistance Force (Isaf), refused to give further details of the planned offensive, but said it would be on a "similar" scale to the ongoing operation in Helmand province, where 15,000 troops have been deployed.
Another 850 extra troops are set to be sent to Afghanistan after German politicians voted in favour of extending the mission there by another year.
"This incident is likely to be scrutinised in Germany, where the deployment of troops in Afghanistan has raised controversy," Al Jazeera's Bays said.
Twenty-two German soldiers have been killed by fighting or attacks in Afghanistan since 2001 and another 138 wounded, according to the German defence ministry.