Local leaders have started reaching out to supporters of the group known by its German acronym, Pegida, or the Patriotic Europeans Against the Islamization of the West, to listen to their complaints and try to forestall the movement. Although still largely confined to Dresden, it has found sympathizers in other cities across Germany.

Front pages of German newspapers showed Lutz Bachmann, leader of the anti-immigrant group Pegida, posing as Adolf Hitler in an image found on his Facebook page.German Anti-Immigrant Figure Quits Post After Posing as HitlerJAN. 21, 2015

Tens of thousands rallied Monday in Dresden in support of Pegida, a group that opposes immigration. The poster reads, “Mrs. Merkel here are the people!”Big Anti-Immigration Rally in Germany Prompts CounterdemonstrationsJAN. 12, 2015

The grass-roots movement, representing a swath of people fed up with the political and media culture in Germany and complaining that their elected officials are not listening to them, has grown swiftly since emerging in October, taking German leaders by surprise. But concerns about Pegida’s roots, as well as its support from neo-Nazis and extremists, have tainted the group’s motives and created a split among elected officials over how seriously they should take some of the group’s grievances about the country’s immigration and social fabric.

In Dresden, an estimated 25,000 protestors took to the streets to protest Germany’s immigration policies. Video by Erik Olsen on Publish Date January 12, 2015. Photo by Sean Gallup/Getty Images.

In a surprise move, Sigmar Gabriel, deputy to Chancellor Angela Merkel, turned up in the audience at a forum of about 200 people on Friday night to listen to supporters and critics of the movement. The goal of the event was for the two sides to engage each other in dialogue, under the slogan, “Why (not) go to Pegida?”

“I would not speak with organizers who move in neo-Nazi circles,” Mr. Gabriel, a member of the center-left Social Democrats, said after the two-hour event. “But the people who go there, and those who are frustrated with politics, of course we have to speak with them.”

The Friday forum was the third such event in Dresden last week. Thomas de Maizière, the country’s interior minister, and the governor of Saxony State, Stanislaw Tillich, both members of the chancellor’s center-right Christian Democrats, took part in similar discussions with Pegida supporters and their opponents.

The moves are a shift since Ms. Merkel’s New Year’s address, which urged Germans to shun the Pegida rallies and their organizers, who she said had “prejudice, coldness, even hatred in their hearts.” The chancellor’s speech has since become a source of derision at Pegida marches and rallies, amid calls for more power for the people and limits to the number of immigrants who are allowed into the country. Supporters also denounce what they perceive as a growing threat of Islamic extremism to their culture.

Even after last week’s outreach events, thousands again crowded the cobbled square outside Dresden’s opera house on Sunday, waving German flags and calling for changes to immigration laws. The event was the first time the movement had gathered since the police banned all demonstrations in this eastern German city for 24 hours last week, after reporting terrorism threats against a Pegida leader who was forced to step down when an image of him dressed as Adolf Hitler emerged.

About 17,000 supporters turned up, and their message was the same as it had been: dissatisfaction with their local and national governments.

A man who would give only his first name, Bernd, said his main reason for joining the movement was his belief that elected officials were not listening to the people.

“We need a new immigration law,” he said, holding a placard appealing for unity among the “Patriots of Europe.” “We have too many poor people. We need a change in the whole political process.”

Many of the supporters’ grievances are similar to those of the early Tea Party movement in the United States, though their goals for government could not be more different: Tea Party supporters want less government, while Pegida supporters are calling for more government involvement in their lives. Both, though, share a disenchantment with their elected leaders and the political system.

Hans Vorländer, a professor of political science at Dresden’s Technical University, interviewed 400 people at several Pegida marches between Dec. 21 and Wednesday, following them over the weeks to identify better who they are and what they stand for. He described the movement as driven by a feeling of “we down here and you up there.”

His study found that a majority of supporters were middle-class, middle-aged men with solid incomes. Only a quarter of the 400 people surveyed openly expressed fears of Islam, despite the name they convene under. Instead, many named a general dissatisfaction with politics and their elected leaders as a key reason for taking part in the marches, forcing officials to listen to their complaints.

Only 49 percent of the 3.4 million eligible voters in Saxony turned out in last year’s state elections, well below the national average of about 71 percent.

“The political system is at a crossroads,” Mr. Vorländer said. “They have to address issues of social composition, social cohesion and social integration.”

Groups and individuals involved with Pegida — and uncertainty about who is behind the movement’s origins — have made many politicians leery, but also concerned that the group could grow and taint 70 years of history in which Germany has tried to promote an image of tolerance and inclusion.

But after the photo of the Pegida leader posing as Hitler and weeks of denials of any Nazi sympathies by organizers despite chanting by a far-right bloc at many of the 12 previous marches through Dresden and in other cities, some said the need for dialogue appeared even more critical. Not only for the country’s social cohesion, they said, but to prevent a tarnishing of its reputation abroad.

“The perception abroad right now is very strong that Germany is seeing a growth of similar far-right movements to those in Sweden or the Netherlands,” said Mr. Gabriel, the deputy chancellor. He added that many people had approached him last week during his visit to the gathering of world leaders in Davos, Switzerland, to ask what was “going on in Germany.”

“I do not believe that there is more far-right extremism in Germany,” Mr. Gabriel said. “But there is certainly a growth of populism on the right which has to do with parties and the social elites too often believing that their debates are identical with those of normal people.”

But Frank-Walter Steinmeier, Germany’s foreign minister, warned Sunday in comments to the mass-circulation weekly Bild am Sonntag that Germans were underestimating the damage that Pegida’s “xenophobic and racist slogans and placards have already had.”

“Whether we want it or not, the world is watching Germany with great attention,” Mr. Steinmeier said.

The New York Times