BERLIN >> The stabbing of a politician overseeing refugee affairs in Cologne and a reference to concentration camps at an anti-immigration rally of 20,000 people have set off new fears that anti-immigrant sentiment is taking a sharper turn in Germany, even as pressure mounts on Chancellor Angela Merkel’s government over its handling of Europe’s migrant crisis.

The violence has spurred a new debate about whether hate speech, which in Germany is routinely subject to investigation and prosecution when spoken or printed, should be removed from social media. Several politicians have called on Facebook in particular to take down hateful language.

For the first time, the government has openly accused the far right of organizing anti-immigrant rallies, while also calling on Germans to "stand together."

On Wednesday, the head of Germany’s Central Council of Jews, Josef Schuster, noted that "the incitement against refugees has reached a level which is absolutely horrifying and completely unacceptable."

Local officials largely responsible for housing and feeding migrants are complaining of ever greater belligerence and threats; the mayor of Leipzig, Burkhard Jung, last week found graffiti saying, "Jung, we will get you."

A mock gallows appeared at an anti-immigrant rally last week, with labels indicating the nooses were intended for Merkel and her deputy, Sigmar Gabriel, leader of the Social Democrats. On Wednesday, the police reported that a mock gallows was erected last weekend some 400 yards from a migrant shelter near Magdeburg.

The actions and words have set off a level of concern that was not evident in Germany a year ago when a small but vocal anti-immigrant movement took hold in Dresden. At the time, the government appeared anxious not to draw attention to the group by discussing its activities, while pro-immigrant forces also turned out in force to counter the anti-immigrant sentiment.

But in the months since, more episodes of violence against migrants and migrant shelters have been reported in Germany than in any other European country — 400, or more than one attack a day on migrant shelters so far this year — with many occurring before tens of thousands of people from the Middle East and Africa began flooding in through Bavaria this summer.

The human wave, which could amount to 1 million newcomers this year, has taxed resources and the patience of many Germans, who are expressing growing anxiety about immigration policies, according to public opinion polls.

Many politicians are wondering how to accommodate the arrivals as they run out of buildings, temporary shelters and even beds. A letter signed by 215 mayors in North Rhine-Westphalia on Wednesday asked Merkel and the state governor, Hannelore Kraft, for help and said even the supply of tents was almost exhausted.

At the same time, Europe has failed to reach a common solution to stem or control the flow of people to the Continent. On Wednesday, the president of the European Commission, Jean-Claude Juncker, summoned leaders from Austria, Bulgaria, Croatia, Macedonia, Germany, Greece, Hungary, Romania, Serbia and Slovenia to a meeting on Sunday to address the continuing flow of people through the Balkans, as temperatures drop and accommodations along the migrant trail through that region remain inadequate.

In Germany, the stabbing last Saturday of Henriette Reker, 58, a senior official responsible for welfare and thus migrants in Cologne, stunned Germans. Reker was stabbed several times in the neck during her last day of campaigning to become mayor of Germany’s fourth-largest city, and four other people were wounded.

Her assailant, a 44-year-old man, was identified by the police as someone with a far-right background. On Monday the federal prosecutor’s office, which took over the case, said that the accused "wanted to send a signal about what he sees as the ever increasing number of refugees admitted to the country."

Within hours, politicians from all over the state, Germany’s most populous, held a vigil near Cologne’s cathedral. "We are showing that democracy stands together, across party lines," said Kraft, the governor. "And that we do not permit violence to take effect."

Officials drew a straight line between hateful language and violence.

"In Cologne, somebody felt called upon to do exactly what he gets to read every day" on social media, said Armin Laschet, a leader of Merkel’s Christian Democrats in North Rhine-Westphalia, where Cologne is.

The federal interior minister, Thomas de Maiziere, on national television on Sunday called for Germans to spurn extremists spreading "poison" in the country. Justice Minister Heiko Maas has called on all Democrats to stick together.

But on Monday in Dresden, some 20,000 Germans rallied for PEGIDA, the anti-immigration, anti-Muslim group that emerged there a year ago. Its marches eventually attracted 25,000 people last winter before the group faded amid personal quarrels and unease at Hitler poses and anti-foreigner language on the Web from the movement’s founder, Lutz Bachmann.

With the migrant crisis, however, the movement has garnered fresh attention, even if its appeal remains largely limited to Dresden and surrounding parts of rural Saxony. Defying de Maiziere’s and the chancellor’s warnings to stay away, supporters flocked under heavy police presence on Monday evening to the city’s Theatre Square.

Bachmann told the crowd, "We came to stay, and we will stay to win."

Even Bachmann, however, intervened and disowned a Turkish-German writer’s speech on his website, after the writer launched an attack on establishment politics. The writer, Akif Pirincci, asserted that the government wanted German critics of its migrant policy to leave the country, to which the crowd chanted, "Resistance, resistance!"

His speech was hard to understand as words echoed off darkened buildings around the square, but the German news media quoted the author as saying that, for the government, "there are of course other alternatives" to get rid of critics. He then was reported to have added: "Unfortunately, the concentration camps are closed right now."

The authorities are investigating whether Pirincci is liable to hate-speech charges.

An estimated 15,000 PEGIDA opponents turned out in Dresden on Monday. Only the presence of almost 2,000 police officers from six German states prevented major clashes between the two groups.

Schuster, the leader of the Council of Jews, did not refer explicitly to Pirincci when in Thursday’s editions of the Berlin newspaper Tagesspiegel he appealed to the German authorities "to exhaust all legal possibilities to prevent rallies where calls to violence are issued."

The attack on Reker showed, he added, "where all this can lead."

Reker, an independent candidate backed by the Christian Democrats and two other parties, won Sunday’s mayoral election and the authorities said she would most likely make a full recovery. But reports that her attacker had ties to the far right in Bonn in the 1990s raised fresh doubts about the vigilance of Germany’s security services when it comes to right-wing extremism.

For years, the authorities failed to uncover a right-wing cell eventually associated with the killing of 10 immigrants from 2000-07. A lone survivor of that group has been on trial for more than two years, with the proceedings in Munich expected to continue into next year at least.