The 18-year-old, who killed himself after the attack, had a Glock pistol that police believes he may have bought on the so-called dark net.
Meanwhile police in Munich have announced the arrest of a 16-year-old Aghan friend of David Ali Sonboly.
They say he is under investigation for not reporting Ali Sonboly’s plans.
“There is a suspicion that the 16-year-old is a possible tacit accomplice to the attack,” a statement on Munich police’s Facebook page says.
The statement goes on to say that the youth reported to police immediately after the shooting on July 22, and was interviewed as somebody with a connection to Ali Sonboly.
In the course of the interviews, they discovered discrepancies in his statements.
Police say they are now investigating the teenager on suspicion of failing to report a planned crime.
The investigations will have to show to what extent he was responsible for a Facebook post inviting people to meet at a cinema complex near the main railway station in Munich.
Ali Sonboly himself had put up a Facebook post before his attack, inviting people to come to the McDonald’s restaurant where the shooting began.
Seven of the dead in the shooting at the Olympia shopping centre were teenagers – two Turks, two Germans, a Hungarian, a Greek and a Kosovan.
A further 35 people were injured, but only four of them have bullet wounds – many were hit fleeing the scene.
According to the state government officials, the victims of the attack had not been specifically targeted and were not classmates of the gunman.
Also they did not include three youths allegedly involved in bullying Ali Sonboly when he was at school.
Head of Bavaria’s criminal police Robert Heimberger said Ali Sonboly had been planning the attack since he paid a visit last year to the town of Winnenden – the scene of a previous school shooting in 2009 – and took photographs.
Robert Heimberger said it was likely the Glock pistol – which had been reactivated – was bought on the “dark net” market, an area accessible only with the use of special software. It had been a theatre prop.
Ali Sonboly was said to be a keen player of “first-person shooter” video games.
Robert Heimberger added that the parents of the gunman remained in shock and were not able to be interviewed.
He also said police had not found the manifesto of Norwegian mass killer Anders Behring Breivik when they searched Ali Sonboly’s room at his parents’ flat.
A day earlier, officials had raised the possibility of a link to Anders Breivik, whose own attack was carried out five years earlier to the day.
As to Ali Sonboly’s state of mind, a spokesman for the Munich prosecutors’ office told a news conference that the gunman had spent two months as an inpatient at a mental care facility in 2015 and was afterwards treated as an outpatient.
“The suspect had fears of contact with others” and also depression, Thomas Steinkraus-Koch said.
However, there was no evidence of any political motivation.
Senior German politicians have called for tighter controls on the sale of guns in the wake of the shooting at the Olympia shopping centre.
Munich’s police chief has urged the media to respect the privacy of those affected by the attack on July 25, when schools reopen.
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