BERLIN—A senior German government minister said on Tuesday that Berlin had little choice but to let in thousands of migrants every day as a backlash against Berlin’s open-door refugee policy among voters and within the government intensifies.

“We simply can’t control the internal borders in Europe. Once people have arrived in Europe, they are unstoppable,” Finance Minister Wolfgang Schäuble said at a conference in Berlin.

“We won’t be able to stop them, forget about this,” he said, referring to Germany’s 1,800-mile long border with other European Union nations. “The problem can only be solved by better controlling access to Europe.”

German Chancellor Angela Merkel is facing growing public skepticism and an open revolt among members of her government over her decision, early last month, to let in thousands of migrants and asylum seekers from the Middle-East, Afghanistan, and Africa.

Conservative allies of the Chancellor in Bavaria, the affluent south-German state that is the main entry point for migrants traveling through Austria, have become increasingly strident in their rejection of Ms. Merkel’s refugee policies. With opinion polls showing voters turning against the chancellor, Bavarian State Premier Horst Seehofer threatened to take the federal government to the constitutional court for sanctioning what he said were thousands of illegal entries by migrants into Germany every day.