"We can't shut the borders. If you build a fence, people will find another way. There is no such thing as stopping the arrivals," Merkel told interviewer Anne Will on her political talk show.
But Merkel promised that Germany would push for the European Union to do more to fight the reasons for flight abroad and to share the burden of the refugee crisis more evenly among countries.
The Chancellor would not be drawn on how long it would be until the country saw progress on these questions – although she acknowledged that "It will be a while. Longer than some people are hoping for".
And she added that "no one" could reliably estimate how many people would arrive in Germany in the future seeking asylum.
Sinking poll numbers
Merkel is doubling down on her commitment to the refugees arriving in Europe even as her own popularity sinks.
Just 47 percent of respondents to a survey published by broadcaster RTL and Stern magazine on Wednesday said they would vote for Merkel if the Chancellor were directly elected – a two-percent drop on the previous week.
Merkel's Christian Democratic Union and their Christian Social Union allies in Bavaria had 39 percent support in the poll, losing one percent on the previous week.
The big winners of the survey were right-wing populists AfD, who gained two points.
Tough words in Brussels
But the Chancellor is demanding that her troops remain in line by making the refugee crisis a question of principle.
Her fierce belief in the rightness of her course was on display on Wednesday in exchanges with centre-right MEPs in Brussels in a private meeting before her joint address to the European Parliament with French President Francois Hollande.
"The eastern Europeans – and I'm counting myself as an eastern European – we have experienced that isolation doesn't help," she said, sources told Politico.
"It makes me a bit sad that precisely those who can consider themselves lucky that they have lived to see the end of the Cold War now think that one can completely stay out of certain developments of globalization."
Merkel acknowledged that eastern European countries were being asked to catch up very fast on developments in tolerance and diversity that had taken the West decades.
But "when someone says, 'this is not my Europe, I won't accept Muslims...' then I have to say, this is not negotiable," she insisted.
And she repeated her message that Europe "won't be able to transform into a fortress," looking back at the fall of the Berlin Wall 25 years ago.
"The refugees won't be stopped if we just build fences. That I'm deeply convinced of, and I've lived behind a fence for long enough," she said.