BERLIN - The burning newspapers placed outside the home of five asylum seekers in Brandenburg an der Havel, a small town near Berlin, prompted a swift response. Germany's foreign minister called the incident last month, in which nobody was injured, a ''cowardly act of arson.''
It happened the week authorities revealed a sharp rise in the number of crimes against asylum seekers or refugee homes during the first half of the year. In the six months ending in June, some 202 incidents were reported - more than during all of 2014.
But the apparent rise in hostility toward refugees has been countered by an outpouring of sympathy and support for people seen as desperate victims of poverty or violence.
In recent months, Germans have flocked to join welcome committees for asylum seekers, many of whom come from Syria, Iraq, Eritrea and the Balkans and see wealthy Germany as a kind of promised land. Students, retirees, and even one conservative lawmaker have taken refugees into their homes.
Others have created websites to organize car rides for refugees wanting to come to Germany for accommodations and jobs.
''We felt we just had to do something to assist these people, because they deserve our help,'' said David Jacob, a 24-year-old student from Berlin who cofounded workeer.de, a site that matches refugees and employers. Launched at the end of July, the site already has over 1,000 registered refugees and 450 employers.
The starkly differing reactions to the influx of refugees points to an increasing polarization in Germany, with growing acceptance of outsiders by a majority but a persistent and possibly radicalized minority fearful of all things foreign.
Authorities have attributed about 173 antirefugee incidents, including eight cases of arson, in the first half of the year to far-right sentiment.
For Germans, the arson in particular has stoked grim memories of fatal firebombings in the early 1990s, when many in the country and abroad feared that overt racism was again going mainstream less than half a century after the defeat of the Nazis.
Reflecting the national angst, German weekly Der Spiegel recently asked ''Is the Ugly German Back?'' atop an article about racist attacks against refugees. The Munich-based daily Sueddeutsche Zeitung warned that Germany could be on the verge of ''exploding'' again.
Experts say it would be wrong to downplay any violence against foreigners, but point to another figure that puts the racist incidents in context: Germany received 77,109 asylum requests in the first six months of 2014, and in the same period this year the figure had risen to 179,037.
In other words, for every 1,000 refugees there was one incident - a similar ratio to the same period last year. Most of the recorded incidents were threats, property damage, or the display of forbidden symbols at demonstrations.
Meanwhile, the majority of Germans have been openly supportive of refugees. In Buch, a downscale suburb of Berlin, one Eritrean asylum seeker said the only time he had witnessed any hostility was when a far-right protest occurred outside the gates of his refugee shelter.
''But there were many, many more people protesting for the refugees,'' said the 32-year-old, who gave his name only as Mehari out of concern for his family in Eritrea.
Hajo Funke, a professor of political science at Berlin's Free University, said, the attitude of most Germans toward foreigners nowadays is profoundly different from what it was a couple of decades ago, when immigrants were considered temporary residents only and citizenship was still tied to blood lineage.
''There has been an immense change in society. Germany has become a more open, liberal country," said Funke, an expert on Germany's far-right movement. He said polls show about two-thirds of the people say they are willing to invest time or money to help refugees.
When hundreds of asylum seekers were camped outside Berlin's central reception center for refugees last week in searing August temperatures, locals spontaneously used social media to organize deliveries of water, ice cream, and toys for children.
Refugee supporters say there's no cause for complacency, however. Robert Kusche, who runs a counseling service serving for victims of hate crimes in the eastern city of Dresden, said many attacks don't show up in official statistics because refugees don't believe it's worth reporting minor incidents such as spitting or shoving in the street.
Kusche said groups such as PEGIDA, which stands for ''Patriotic Europeans against the Islamization of the West,'' had tapped into a lingering fear of foreigners among some parts of German society. While PEGIDA's weekly protests have dwindled to several thousand from their peak of 25,000 in January, its supporters have been actively setting up Facebook pages opposing the opening of refugee shelters and flooding the comment pages of news websites with derogatory messages about foreigners.
''We need a strong sign that this won't be tolerated,'' said Kusche.
Last week, Anja Reschke, a journalist for Germany's public broadcaster ARD, delivered just that, receiving widespread applause for an on-air comment slamming what she called the ''little racist nobodies'' who express hatred of refugees online. The video was watched almost 8.7 million times on Facebook alone.
Despite the current support for refugees, some are nervous. ''Far-right extremists are exploiting concerns among parts of the population and this is leading to violence,'' said Funke. ''The danger is that this will take the shape of terrorism.''
For now, most refugees appear to feel secure in Germany.
Hassan Salameh, a 30-year-old pharmacist who fled Aleppo with his mother and two sisters, said he considers himself lucky to be in Germany.
''Actually it's the second homeland for us. The people are very lovely, very helpful,'' he said at a refugee shelter in Spandau, on the outskirts of Berlin.
Still, one incident stuck in his mind.
''We were walking together with my family and someone made like this,'' said Salameh, making a cutting gesture across his neck. ''But they don't try to make action, it's just a sign. We ignored this and continued our walk in the park.''
Elias Meseret in Addis Ababa, Ethiopia, and Olga Syrova in Berlin contributed to this report.