Mattias Karlsson, who is in charge of the Sweden Democrats for the foreseeable future after the party's leader Jimmie Åkesson announced on Tuesday that he was extending his sick leave, described Nazism as "terrible" in an interview with Swedish broadcaster SVT on Tuesday.
But he added that he felt the threat from Islamism today was "perhaps greater than from Nazism".
The word Islamism broadly refers to the ideology that says a country's government and society should operate in accordance with Islamic laws.
"One must of course take all ideologies seriously and fight them in every way," said Karlsson on Tuesday.
The Sweden Democrats have roots in neo-Nazi movements of the 1980s and 1990s but have sought to distance themselves from their background and to establish themselves as a mainstream political party.
The anti-immigration group is currently the third largest group in Sweden's Riksdag, scoring almost 13 percent of the vote in the last general election.
"If you look at what is happening in the world right now, you cannot hide the fact that Islamism is a major threat to human rights and democracy throughout the world," added Karlsson in his SVT interview.
His comments have provoked outrage among Jews in Sweden, who are marking the 70th anniversary of the liberation of Nazi extermination camps in occupied Poland.
Lena Posner-Körösi, chairwoman of the Jewish community in Stockholm, whose father emigrated to Sweden from Germany in 1939 told The Local:
"It is completely out of line to start comparing threats - especially on a day when we are commemorating Jews. We still have Holocaust survivors among us and they have some very scary testimonies."
"As we make this commemoration, we want people to recognize evil in the world and to know that this can happen to any group, not just Jews. For him [Mattias Karlsson] to talk about the threat of Islam as he has done is very dangerous and shows he hasn't learnt anything. And yes, he is from a group with a Nazi past."
Stockholm's Great Synagogue where Jews are gathering on Tuesday evening. Photo: TT
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Leading Muslim commentators have also criticized Karlsson's comments.
"It is not the first time that he has talked about the dangers of Islam and a multicultural society," Zachariah Zouhir who is chairman of the African Swedish National Association told The Local.
"He is seeking to polarize different groups. But actually what happened to the Jews is happening to Muslims now. We are being persecuted in Europe. We may not be being killed, but there are attacks on our mosques, women are being attacked in the street and governments are getting tougher on us."
He added that the Muslim community would also be remembering Jews this week as part of the global commemoration of the date Jews were freed from the Auschwitz-Birkenau concentration camps.