BERLIN — German leaders responded on Wednesday to persistent violence led by far-right extremists against the increasing number of foreigners seeking asylum, with the chancellor and the president making visits to refugee reception centers to send a message of acceptance.

“There is no tolerance for those people who question the dignity of others, there is no tolerance for those who are not willing to help where legal and human help is required,” Chancellor Angela Merkel said in Heidenau, a town in eastern Germany, where she was jeered by a group of about 50 people when she arrived.

Germany, along with Austria, France and Sweden, has taken in the bulk of the hundreds of thousands flocking to Europe, but countries across the Continent are struggling to cope with the influx.

In Hungary, a day after the police said that 2,533 immigrants had entered the country from neighboring Serbia on Tuesday, the highest one-day figure this year, officials planned on Wednesday to send the army, mounted police and dogs to its southern border to confront the migrants, Reuters reported.

The Hungarian police sought to quell unrest at a reception center in the border region of Roszke, German news media reported, with the broadcaster ARD showing images of what appeared to be clouds of tear gas in an area crowded with migrants.

Most of the migrants entering Hungary have no plans to stay there, and they are instead passing through on their way to Germany or to other countries in the European Union that are seen as more desirable.

Yet many countries, including Germany, are struggling to process the number of asylum seekers, leading to unrest and difficult conditions at overcrowded reception centers.

“Given what we have all been forced to see here, I would like to recall that the humane and dignified treatment of every individual who comes to us is part of Germany’s national identity,” Ms. Merkel said after visiting the center in Heidenau, near Dresden, that was the site of violent protests over the weekend.

Several hundred neo-Nazis and members of the far-right National Democratic Party threw stones and bottles at the police and shouted “Heil Hitler” during the protests in Heidenau. Ms. Merkel called the clashes and anti-immigrant protests “shameful and offensive.”

Pledging to “do everything possible to make clear that Germany helps where help is needed,” she said that when Parliament reconvenes in September, legal changes would be made to help cope with the influx of asylum seekers.

Graphic The Global Struggle to Respond to the Worst Refugee Crisis in Generations Eleven million people were uprooted by violence last year. Photos and maps show the international response to what has become the worst migration crisis since World War II.