At counter-demonstrations and on social media, opponents have mobilized against the far-right group which claims Germany is being overrun by Islamic extremists.
President Joachim Gauck, who was a pro-democracy pastor in communist East Germany, devoted his annual Christmas speech to a forceful appeal for compassion and openness toward asylum seekers.
Faced with the emergence of the group "Patriotic Europeans Against the Islamization of the Occident", or PEGIDA, which has been staging weekly marches, Gauck said he was confident the majority of Germans would resist its call.
"That we react with empathy to the plight around us, that most of us don't follow those who want to seal off Germany — that is for me a truly encouraging experience of this year," he said in the address to be broadcast Thursday.
Foreign Minister Frank-Walter Steinmeier welcomed anti-PEGIDA protests, which have drawn thousands, saying most Germans believed those fleeing civil war or persecution should find refuge in the country.
"The Germany that sympathises and helps out is the country that is now required," he told news website Spiegel Online Tuesday.
PEGIDA began in October in the eastern city of Dresden, capital of the state of Saxony, where just 2.2 percent of the population is of foreign origin.
In a manifesto published this month, the group calls itself a grassroots movement that aims to protect "Judeo-Christian values" and urges tolerance of "assimilated" Muslims while opposing the "misogynist and violent ideology" of Islamism.
Its targets also include the "lying media", "political elites" and "multiculturalism".
Opponents say the group uses thinly veiled neo-Nazi rhetoric and is whipping up xenophobic sentiment just at a time when Germany has become Europe's top haven for asylum seekers and the world's number two destination for migrants after the United States.
They stress there is no place for racism in the country that perpetrated the Holocaust.
PEGIDA's first march drew just a few hundred people but last Monday, a record 17,500 turned out, rallying in the city centre and singing Christmas carols.
Smaller clone groups gathered in three western cities, but they only drew up to 200 followers each and were all vastly outnumbered by counter-protests that drew 20,000 nationwide.
The management of Dresden's renowned Semperoper concert house turned the building's lights off as the PEGIDA demonstrators gathered and flew flags outside that read: "Open your eyes", "Open your hearts", "Open doors" and
"Human dignity is sacrosanct", the first line of the national constitution.
The sudden rise of PEGIDA has spooked Berlin, where officials are keenly aware that images of far-right marches in Germany can damage its international standing. Chancellor Angela Merkel last week cautioned Germans against falling prey to any form of xenophobic "rabble-rousing".
The veteran finance minister, Wolfgang Schaeuble, on Wednesday blamed the political class for failing to give a segment of the population the feeling that their interests were being addressed and said officials needed to "listen and present their arguments".
But he told Rheinische Post newspaper that at the same time, politicians must stand up for the values of the post-war republic, including generosity toward asylum seekers.
"What kind of people would we be if we, given our prosperity, turned away refugees?" he asked.
Schäuble joined the president of the German Federation of Industry, Ulrich Grillo, in stressing how badly Europe's top economy needed immigrants to remain competitive.
Grillo, in an interview Tuesday with news agency DPA, blasted the PEGIDA protests, calling participants "neo-Nazis and xenophobes".
He said Germany's rapidly ageing population needed a strong influx of qualified newcomers to support the economy and the social welfare system.
"Considering our demographic development, immigration ensures growth and prosperity," he said.
Meanwhile activists on Facebook and Twitter have mocked PEGIDA and organised opposition against it. Students in Berlin set up the website www.fluechtlinge-willkommen.de (refugees welcome) to offer rooms in shared flats.
Journalist Birte Vogel has launched a blog showcasing projects that help refugees.
And Berliner Ulrike Meier has started volunteering at a home for about 100 asylum seekers in the capital.
She said PEGIDA was an "extremely populist movement" that reflected the thinking among some in the country but "certainly not all of Germany", she said.