JERUSALEM — Prime Minister Benjamin Netanyahu of Israel said on Sunday that his government was encouraging a “mass immigration” of Jews from Europe, reopening a contentious debate about Israel’s role at a challenging time for European Jews and a month before Israel’s national elections.

Speaking the morning after a Jewish guard was fatally shot outside a synagogue in Copenhagen in one of two attacks there, the remarks echoed a similar call by the prime minister inviting France’s Jews to move to Israel after last month’s attacks in Paris. Critics said then that the expression of such sentiments so soon after the Paris shootings was insensitive and divisive. Such sentiments also go to the heart of the complexity of Israel’s identity and its relationship with the Jewish communities of the diaspora, whose support has been vital.

“Jews have been murdered again on European soil only because they were Jews,” Mr. Netanyahu said Sunday in Jerusalem. “Of course, Jews deserve protection in every country, but we say to Jews, to our brothers and sisters: Israel is your home,” he added.

But expressing the unease felt by many Jews abroad over such comments, Jair Melchior, Denmark’s chief rabbi, said he was “disappointed” by Mr. Netanyahu’s call.