SYDNEY, Australia — An Australian lawmaker invoked a Nazi euphemism for genocide on Tuesday, calling for a “final solution to the immigration problem” during a speech in Parliament in which he proposed a national plebiscite on banning all Muslims from entering the country.

“We as a nation are entitled to insist that those who are allowed to come here predominately reflect the historic European-Christian composition of society and embrace our language, culture and values as a people,” said Senator Fraser Anning, a member of Katter’s Australian Party, a small, conservative political party.

“The final solution to the immigration problem, of course,” Mr. Anning said in his first speech since his election, “is a popular vote.”

On Wednesday, leaders from across the political spectrum condemned Mr. Anning’s remarks. Prime Minister Malcolm Turnbull, of Australia’s conservative Liberal Party, called them a “shocking insult” to the millions of Jews who perished in the Holocaust, and he used the moment to appeal to the country’s Muslim population.