Berlin, Germany (CNN) A man arrested over the killing of a senior German politician earlier this month is believed to have links to the far right, prosecutors said Monday.

Walter Lübcke, who was president of the Kassel regional council in central Germany, was shot in the head at close range on the terrace of his home in the small village of Istha, in the early hours of June 2.

The 45-year-old suspect was arrested on Saturday in Kassel based on traces of DNA evidence from the crime scene, according to the Hesse state office of criminal investigation and Kassel's public prosecutor. The suspect has a long criminal record, police said.

The past life and the "openly expressed opinions and public views" of the suspect linked him with the far right, Michael Schmidt, a spokesman for the federal prosecutor's office, told a news conference Monday.