The gunman suffered from depression and had an obsession with shooting sprees like the massacre five years ago by Norwegian rightwing fanatic Anders Behring Breivik.
The shooting began at a McDonald's fast-food restaurant at the Olympia shopping mall near Munich's Olympic stadium shortly before 2130 IST yesterday.
A video posted on social media appeared to show a man dressed in black walking away from the restaurant while firing repeatedly on people as they fled.
Kosovo said three of its citizens were among the fatalities while Ankara said three Turks had died. It was not immediately clear if they had dual nationality.
Most of the casualties are young people aged 15 to 21, Bavarian public television said.
Initially believing three gunmen were involved, the authorities launched a city-wide manhunt, mobilising more than 2,000 police supported by the elite GSG-9 anti-terrorist unit and helicopters.
Munich's main train station was closed and public transport suspended for several hours.
Investigators later found the body of the suspected shooter, who appears to have acted alone and then killed himself with a shot to the head.
His name has not been made public.
Investigations of his home and police files point to "a classic act by a deranged person," Andrae said.
"There is absolutely no link to the Islamic State," he said, adding that the suspect had been obsessed with books and articles about mass killings "linked to maniacs."
He said German investigators have established an "obvious link" between Friday's shooting at a Munich mall and Breivik's mass killings on July 22, 2011.
The city's chief prosecutor also said the suspect had suffered "some form of depression", but voiced caution over reports he may have undergone psychiatric treatment.
On July 14, Tunisian Mohamed Lahouaiej Bouhlel rammed a
lorry into crowds enjoying a firework display on the seafront promenade in the French Riviera city of Nice, killing 84 people including children.
The IS group also claimed suicide bomb attacks at Brussels airport and a city metro station in March that killed 32 people.
The focus on the suspected shooter's motives and background takes place in the context of a fierce debate about Germany's asylum policy and integration of its immigrants.
Hate crimes and attacks against migrants exploded after arrivals, mostly from the Middle East and Africa, reached record levels in 2015.
Some 923 offences against refugee shelters were reported in 2015 including 177 acts of violence, a sharp rise from the previous year, according to figures from the interior ministry.
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