Scenes of far-right protesters chasing down foreign-looking people in violent demonstrations last week against the fatal stabbing of a man, allegedly by an Iraqi, shocked Germany.
Merkel's spokesman Steffen Seibert said it was understandable that such crimes would provoke sadness and concern among the population.
But the marches by “violence-prone right-wing extremists and neo-Nazis have nothing in the least to do with sadness for a person or with concern for a city's cohesion”, he said.
“These people who march and are prone to violence – some have also shamelessly shown their closeness to Nazism – they stand neither for Chemnitz nor for Saxony overall, neither are they 'the people',” said Seibert, referring to a popular “We are the people” chant used by far-right protesters.
“We must make that clear to them,” be it through political or legal means, he said.
“Every citizen can also raise his or her voice to clearly show them their attitude against hate, against the attempt to divide this country.”
But the criticism of the right-wing extremist protesters was immediately rejected by far-right party AfD.
“An entire state and its people are vilified here in general because there is a distinct and understandable resentment about the circumstances,” Jörg Meuthen, AfD co-chief said at a street festival in Bavaria.
After a weekend of rival protests in Chemnitz that saw far-right demonstrators vastly outnumber counter-protesters by 8,000 to 3,000, calls have grown for the silent majority to mobilize.
On Sunday, Foreign Minister Heiko Maas urged Germans to “get off our sofas and open our mouths” against xenophobia.
Later on Monday, several left-leaning and anti-fascist punk bands, are due to perform in a free concert under the motto “there are more of us”, with several thousands expected to join in the protest against racist violence.
A “window demo” call has also gone out on social media for those who cannot make it to Chemnitz to hang a colourful poster on the window or balcony to show their support for the anti-racist cause.
The unrest has once again put the spotlight on Merkel's liberal refugee policy that led to the arrival of more than one million asylum seekers since 2015.
Resentment against the newcomers runs particularly deep in Saxony state, where Chemnitz is located, and the AfD has won strong support in the region with its anti-migrant campaign.
Surveys suggest it is poised to become Saxony's second biggest party in next year's regional elections.