Angela Merkel has said Germany must rigorously fight rightwing extremism after the murder of a prominent politician.

The arrest of a man with suspected far-right sympathies over the shooting this month of Walter Lübcke, a regional ally of Merkel known for his pro-migrant views, shocked Germany and prompted calls for a more proactive government response to anti-immigrant extremists.

The chancellor, speaking in Dortmund on Saturday at an annual gathering of Protestant churches, said rightwing extremism must be fought “without any taboo”.

“Otherwise we will have a complete loss of credibility,” she said, adding that the government took the issue “very, very seriously”. Her interior minister, Horst Seehofer, made similar comments last week.

Germany is home to 12,700 potentially violent far-right radicals, domestic intelligence agency BfV estimates, and a Civey poll showed 60% of Germans think the government is doing too little to oppose them.

Lübcke, the head of the district government in Kassel in the state of Hesse, was shot in the head at close range on the terrace of his home.

A 45-year-old man was arrested at the weekend.