A spokesman for the German Federal Prosecutor's office on Monday said investigators suspected a far-right motive behind the murder of Walter Lübcke, a local politician from the western state of Hesse.
On Saturday, special police units arrested a 45-year-old man in connection with the killing in the central city of Kassel, 160 kilometers (100 miles) northeast of Frankfurt. Authorities said the arrest "was based on a DNA match."
The individual was then brought before an investigating judge on Sunday and remanded in custody. Investigators said they would only release further information about the suspect and the ongoing probe next week.
Lübcke, the head of the regional council in Kassel, was found lying on the terrace of his home in Istha on June 2. He was declared dead two hours later.
According to the autopsy, the 65-year-old was killed by a bullet fired at close range. Suicide had been ruled out.
Lübcke, who represented Chancellor Angela Merkel's ruling conservatives, had received death threats, possibly in connection with his pro-migrant views.
Amid opposition to Germany's decision to allow a huge wave of Syrian refugees and other migrants to enter the country, the politician declared it was morally right to give protection to those in need.
Police have also looked into hateful social media comments posted after Lübcke's death.
A week after the murder, a man traveling on a tourist ferry in Eastern Friesland was arrested but was later released without charge.
Lübcke's funeral service, on Thursday, was attended by 1,300 people.
dv/jm (dpa, AFP)