The German leader, who cut short her summer holiday to speak after a string of Islamist attacks rocked the country, said the entire continent was being “ravaged” by terrorism.
She described recent attacks in Ansbach, Wurzburg and Munich as “horrifying and depressing” but insisted Germany would not turn its back on people fleeing the Middle East.
In the wake of the killings, Mrs Merkel said Germany now needed a better “early warning system” to spot radicalised Muslims among the newly-arrived migrants.
She said the central government would “redouble its efforts” against the threat, increasing staff numbers and resources for security services.
She said: “The terrorists want to make us lose sight of what is important to us, break down our cohesion and sense of community as well as inhibiting our way of life, our openness and our willingness take in people who are in need.
“They see hatred and fear between cultures and they see hatred and fear between religions.
“We stand decisively against that.”
She added that Germany would “stick to our principles” and “give shelter to those who deserve it”.