"We are looking for a perpetrator," said chief prosecutor Horst Streiff after the death of city administrative chief Walter Lübcke, who was 65.
Streiff stressed that there was no evidence pointing to suicide.
Lübcke, of German Chancellor Angela Merkel's centre-right CDU party, was found around 0:30 am local time Sunday on the terrace of his home in Wolfhagen, near Kassel in the central state of Hesse.
He had been shot in the head at close range with a handgun, police said.
His CDU party said in a statement that Lübcke a married father of two, had "never been afraid to speak his mind".
Walter Lübcke in 2012, announcing the decision to build a sewer pipeline. Photo: DPA
Germany's top-selling daily Bild pointed out that Lübcke had in 2015, during a mass influx of migrants to Germany, strongly spoken out for the rights of refugees, drawing anger from far-right activists.
Hesse state criminal police chief Sabine Thurau said however that currently there was no evidence of a link between those comments and his death, and that a 20-officer investigation team was searching for a possible motive and a suspect.
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