A suspected far-right extremist carried out the attacks on two shisha bars in western Germany, killing at least nine people, officials say.
Chancellor Angela Merkel said there were many signs the attacker in the city of Hanau had acted out of racism.
Federal prosecutors are treating the case as terrorism. Some of those killed were believed to be of Turkish origin.
The 43-year-old suspect killed himself, police say. He was found dead at his home along with the body of his mother.
Local media have identified the suspect as Tobias R, a German citizen. The Bild tabloid reports he had a firearms licence, and that ammunition and gun magazines were found in his car.
Authorities are examining a video that appears to be from the suspect, posted online days before the attacks, in which he expresses right-wing conspiracy theories. Bild said he had also left a letter of confession.
The attack comes amid growing concerns about far-right violence in Germany. Speaking in Berlin, Mrs Merkel said: "Racism is a poison. Hate is a poison and this poison exists in our society and is already to blame for many crimes."