Prosecutors on Monday said they suspected an extremist motive in the assassination-style shooting of Kassel city administration chief Walter Lübcke, 65, on June 2nd.
A suspect identified as Stephan E., 45, is in custody, with prosecutors saying he has multiple links to the far-right scene.
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If the motive is confirmed, the murder would be post-war Germany's first killing of a politician by a far-right perpetrator.
Interior Minister Horst Seehofer, who called the killing an "alarm bell" for Germany, acknowledged Tuesday that "far-right extremism is a significant and serious danger for our society".
For the left-leaning Taz daily, the case "must be a turning point".
"We must speak about far-right terror, and in a very different way than before," it warned, stressing that words must also be backed up by action to counter the threat.
"We need a rigorous procedure against right-wing militants and their structures -- and also against the digital mob and the verbal lashing from (Islamophobic movement) Pegida to (the far-right party) AfD."
Markus Nierth, who had quit his voluntary mayor post in a village after receiving threats from the far-right over his pro-migrant stance, told the daily Berliner Zeitung the killing revived memories of the weeks and months both he and his wife spent in fear.
"'We'll get you at some point' - that's the message of this case," he said.
Nierth warned that politicians who call for "more understanding for the far-right" fringes need to wake up.
"In Walter Lübcke, a key inhibition threshold has been crossed. Suspected far-right terrorists have now done what they have dreamt about for years in their perverse fantasies of violence."
'Hate seeping in'
Investigators into Lübcke's murder had initially said there was no evidence of an extremist motive, before arresting Stephan E., a former member of the neo-Nazi NPD, more than two weeks later.
Observers said the initial failure to draw a link to the far right was chillingly reminiscent of investigations into the killings of nine Turkish and Greek-born immigrants by the far-right militant group National Socialist Underground (NSU).
Investigators into the NSU murders that took place from 2000 to 2007 were looking in the wrong direction - from seeking blood feud motives to searching for gambling debts or alleged drug deals on the part of the victims - to explain the killings.
In the Lübcke case too, "some investigators did not want to admit the obvious - that a politician was liquidated here because he stood up for Germany's constitution," said Süddeutsche Zeitung.
Urging action, the daily noted that the like-minded militants were openly applauding the killing on social media.
"Hate is seeping from the fringes into the middle of society.”
More than 12,000 far-right extremists across the country are rated dangerous in official statistics.
Painting a dark picture of the reaches of far-right extremism, the daily also cited several cases in which law enforcers themselves were tainted.
Some 38 investigations were under way against police officers in Hesse state over right-wing extremism issues.
In Saxony state, police were also called out after some used names of NSU perpetrators as their codenames in a deployment during a visit by Turkish President Recep Tayyip Erdogan.
"What must happen before police, prosecutors and domestic intelligence officers recognize that the most dangerous enemy is not on the left but on the right? And sometimes he is even within us," asked Süddeutsche.
Walter Lübcke. Photo: DPA
Experts warned that the situation was very alarming, pointing the finger at the anti-migrant AfD for contributing to an atmosphere of hate.
Extremist expert Gideon Botsch estimated that the "next 12 to 18 months could be extremely dangerous".
"The enemy has been clearly chosen - the AfD contributed to this, Pegida too. All these forces that have officially distanced themselves from violence have contributed a lot to incitement," he said.
CDU lawmaker Michael Brand also accused the AfD of fanning the flames.
"It is true that only the hate and incitement of the last years could have made this possible," he said.
"Anyone who doesn't see that is blind."
Germany's domestic intelligence agency had said that the AfD's "The Wing" (Der Fluegel) grouping, as well as the party's youth organisation JA, were suspected of having ties with the extremist Identitarian Movement.
Online hate posts
Lübcke, a member of Merkel's conservative Christian Democrats, was shot in the head at close range overnight on the terrace of his home near Kassel, 160 kilometres northeast of Frankfurt.
He had passionately spoken out in defence of migrants at the height of Europe's 2015 refugee crisis, drawing the fury of the far right for telling anti-migrant agitators they "could leave Germany".
Since his death, hundreds of posts from social media accounts tied to right-wing extremists have hailed his murder, in turn drawing strong condemnations from President Frank-Walter Steinmeier and other politicians.