BERLIN—German Chancellor Angela Merkel found herself in a public showdown with the sister party to her Christian Democratic Union on Friday, drawing sharp criticism for her opposition to a national cap on newly arriving migrants.

Ms. Merkel spoke in Munich at the annual conference of the Christian Social Union, sister party to the chancellor’s own party. CSU delegates unanimously backed a motion that demanded Berlin limit the number of migrants entering the country.

But Ms. Merkel told the gathering that national responses alone won’t help. Instead, what’s needed is a combination of protecting national borders, seeking European solutions and fighting the root causes of migration and flight, she said.

“With this…we save lives and we will reduce the number of refugees,” Ms. Merkel said. “With this approach to reduce the number of refugees—and in contrast to setting a one-sided upper national limit—we will be able to act in the interest of all.”

She said isolation and a failure to seek solutions aren’t the right response in the 21st century.

“Let’s do this, even if these are big challenges—always eyeing for the good of our country, the good of its people but also for the good of Europe and also as a contribution to make the world a better world,” Ms. Merkel said.

But her speech was sharply criticized by Horst Seehofer, CSU party chairman and Bavarian state governor.

“We firmly believe…Germans’ support won’t be possible in the long run if we don’t get to an upper limit for the immigration of refugees,” he said to thundering applause while a stonily looking Ms. Merkel stood next to him on the stage. “We want to reduce the number of refugees.”

The CSU has sharply criticized Ms. Merkel’s open-door refugee policy over the past months, as its home turf of Bavaria is the main entry point for refugees and other migrants arriving in Germany.

Germany has registered more than 900,000 migrants so far this year, according to the latest figures provided by Bavaria’s interior minister, Joachim Herrmann, on Friday.

The German government officially forecasts 800,000 new asylum claims for this year as a whole, although some officials see the number rising to 1 million, more than 1% of Germany’s population.

An Infratest dimap opinion poll conducted between Nov. 2 and 4 for the ARD public broadcaster showed 71% of Germans surveyed want the government to set a limit on the number of migrants. The same poll showed 49% of respondents were satisfied with Ms. Merkel’s overall policies, a big drop from the 75% expressing satisfaction in April.

Facing criticism from the CSU and concern from the public, Ms. Merkel has repeatedly defended her open-door policy, saying Germany is robust enough to absorb the newcomers, many of whom are fleeing the war in Syria or conflicts in Iraq and Afghanistan while others just want a better quality of life.

But her government has also taken steps to curb the influx, such as cutting cash handouts for asylum seekers, tightening asylum conditions and returning those without a legitimate asylum claim more quickly to their home countries.

Additional measures are under consideration, including limiting family reunifications and speeding up asylum procedures.

Ms. Merkel’s migration policy also faces a test at the annual party conference of her Christian Democrats in December. Powerful Interior Minister Thomas de Maizière and Finance Minister Wolfgang Schäuble have been vocal in calling for a more effective limit on the influx of refugees and other migrants.

There is no indication that the influx of migrants will slow soon, despite the arrival of winter. Around 10,000 people enter Greece from Turkey every day, with many of them heading toward Germany.

Instead of setting an upper limit, Ms. Merkel wants a fixed quota for migrants to be allowed to come to Europe, with such a quota to be agreed upon by European Union member states and Turkey.

Her other coalition partner, the Social Democrats, also oppose a limit on new arrivals, but they see the need to reduce the speed of the influx.

“A nation such as Germany, with more than 80 million inhabitants, isn’t overstrained with 1 million refugees. However, it will be difficult to continue accommodating and absorbing such a number reached in one year over a period of several years,” the party’s chairman, Sigmar Gabriel, and Foreign Minister Frank-Walter Steinmeier wrote jointly Friday for Spiegel Online.

“We therefore must reduce the speed and dynamic of the influx and reduce the number of refugees coming to us in one year,” they said.