A screen grab taken from video footage shows plain clothes police officers taking cover in the car park of the Olympia shopping mall during shooting rampage in Munich, Germany July 22, 2016. [Photo/Agencies]

It was the third major act of violence against civilians in Western Europe in eight days. Previous attacks in France and Germany were claimed by the Islamic State militant group.

"The motives for this abhorrent act have not yet been completely clarified - we still have contradictory clues," German Foreign Minister Frank-Walter Steinmeier said in a statement.

There was no immediate claim of responsibility but supporters of Islamic State celebrated on social media.

"The Islamic state is expanding in Europe," read one tweet.

The gunman, whose body was found on a side street near the mall, was not identified by name but Andrae said he was not previously known to police.

The mall is next to the Munich Olympic stadium, where the Palestinian militant group Black September took 11 Israeli athletes hostage and eventually killed them during the 1972 Olympic Games.

Friday's attack took place a week after a 17-year-old asylum-seeker assaulted passengers on a German train with an axe. Bavarian police shot the teenager dead after he wounded four people from Hong Kong on the train and injured a local resident while fleeing.

The police chief said there were no immediate similarities between Friday's attack and the incident on the train near the southern German city of Wuerzburg.