Merkel was making her first public comments on Friday’s attacks, in which 10 people died including the 18-year-old German-Iranian gunman, who investigators believe had suffered mental problems.
Another 27 were injured in the attack.
The chancellor was speaking after a special meeting of the German security cabinet, which had been called to discuss the shooting spree at a Munich shopping centre and a nearby McDonald’s restaurant.
Police have ruled out a radical Islamist link in the Munich attack.
Police instead believe that the gunman had taken an interest in mass shootings and had been inspired by the massacre in Norway five years ago of 77 people by Anders Breivik.
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