The Central Council of Jews in Germany counts just over 100,000 members — compared with the estimated 520,000 Jews in Germany in early 1933. In the quarter-century since German reunification, Israelis and Jews have flocked to Berlin, where some 45,000 Jews are now said to live.

Ms. Merkel is an unflinching supporter of Israel and Jewish institutions. Schoolchildren learn about the Holocaust, and Germany is promising classes to instruct new arrivals in its standards, customs and beliefs. Events to celebrate Jewish identity and the role of Jews in Germany are common. Leading politicians and city figures gathered on Jan. 7 for the 90th birthday of W. Michael Blumenthal, the former United States Treasury secretary and founding chief executive of the Jewish Museum Berlin, which has counted 10 million visitors since it opened in 2001.

Mr. Blumenthal, born and raised in and around Berlin before his family fled the Nazis, is among the many Americans who have praised Ms. Merkel for welcoming refugees.

Yet even before the migrant influx, synagogues, Jewish schools and other organizations operated only under constant police protection. And now, there is apprehension over the arrival of hundreds of thousands of Muslims raised in countries where anti-Semitism and anti-Israeli sentiment are more virulent than in Turkey, the country of origin for most of Germany’s perhaps four million Muslims.