BERLIN — The recent tension sparked by violent protests in the eastern German city of Chemnitz reached Angela Merkel’s government on Thursday, threatening a truce with the chancellor’s interior minister, who called immigration “the mother of all political problems.”

Ms. Merkel swiftly countered her minister’s comments, calling on Germans to continue working “step for step,” to solve problems related to immigration.

In an interview with RTL television, Ms. Merkel cited the 65,000 people who turned out for a rock concert on Monday in support of the family of a 35-year-old German killed in Chemnitz, as an example of the country’s success in integrating more than one million asylum seekers since 2015.

“We have achieved a lot in taking in refugees, but also face the question of how we deal with them in an orderly fashion,” Ms. Merkel said. “This task simply must be tackled.”