The leader of Sweden’s Jewish community has condemned as “good old rightwing antisemitism” remarks by a far-right leader who said Jews cannot be Swedes unless they abandon their Jewish identity.

Lena Posner Körösi, president of the Official Council of Jewish Communities in Sweden, said the comments conveyed a message that Jews were untrustworthy and could not be considered real Swedes, “exactly like in 1930s Germany” from which her grandfather had fled.

Official Sweden and social media have been in uproar after Björn Söder, secretary of the anti-immigrant Sweden Democrats and deputy speaker in parliament, said Jews could become Swedish citizens but could not be Swedish unless they were assimilated.

Posner Körösi said the remarks showed “the mask is slipping” from the face of Sweden Democrats to reveal the essence of what they stand for.

“I am appalled that Sweden’s third largest party can express itself in this way about Jews and other minorities,” she said. “We have to take them really seriously. This not a small group of fanatics you can dismiss.”

The party took 13% of the vote in elections in September.

Söder claims he was quoted out of context. He also singled out the indigenous Sami people and Kurds in his newspaper interview, not just Jews. “Those who know me when it comes to Jews know I have long had a very strong commitment to both the state of Israel and the Jewish people,” he told Swedish Radio.

Söder had said in a newspaper interview it would be a problem if there were too many people in Sweden “who belong to other nations” and had non-Swedish identities. Paying immigrants to go home would also help to avoid “foreign enclaves” and instead “create a society with a common identity”, he said.

The Sweden Democrats have thrown Swedish politics into turmoil after they used their power of veto two weeks ago to block the government’s budget and force fresh elections in March. The party appears to be thriving on the sense of political crisis, with opinion polls suggesting it is set to increase its share of the vote to between 16% and 18%.

Last week the prime minister, Stefan Löfven, who leads a minority coalition with the Greens, accused the party of being “neo-fascist”. Löfven said he found Söder’s remarks “very, very scary”.

Söder faced calls from parties on the centre left to resign his post as deputy speaker. His remarks were criticised by a leading party colleague as “extremely vague”.

Sweden Democrat leaders have courted controversy in the past by claiming that Zlatan Ibrahimovic, Sweden’s soccer superstar born of Yugoslavian immigrants in Malmö, was not truly Swedish. Niclas Nilsson, party leader in its southern stronghold of Kristianstad, told the Guardian last week: “Zlatan grew up in an area where there were not many Swedes, then he has moved from country to country, so he is a bit Swedish but also cosmopolitan.”

Willy Silberstein, president of the Swedish Committee Against Antisemitism, told TT news agency: “I am a Jew, born in Sweden. I am as Swedish as Björn Söder.”

The Sweden Democrats did not respond to a request for comment.