The Hungarian government and Jewish leaders have roundly condemned a politician who called for a survey of Jewish people thought to pose an alleged "national security risk", accusing him of fearmongering in a country still struggling with the legacy of the Holocaust.

In comments deemed extreme even for his rabble-rousing far-right party, Jobbik, Marton Gyongyosi urged the authorities on Monday to "tally up" the number of Jews in Hungary, especially those in the parliament and government. Such an exercise was, he claimed, "timely" given the conflict raging in the Middle East.

The government denounced the remarks, made in an address to parliament. It said it "strictly rejects extremist, racist, antisemitic voices of any kind and does everything to suppress such voices".

Jewish groups reacted with horror and incredulity at the comments, which they said brought back echoes of a dark past. "I am a Holocaust survivor," Gusztav Zoltai, executive director of the Hungarian Jewish Congregations' Association, told Associated Press. "For people like me this generates raw fear, even though it is clear that this only serves political ends. This is the shame of Europe, the shame of the world."

Jobbik, of which Gyongyosi is deputy parliamentary group leader, is the third-largest political movement in Hungary, holding more than 40 of 386 seats in parliament. Critics say its MPs have made a string of antisemitic, anti-Roma and homophobic remarks – but the party has never made a public appeal for a survey of Hungarian Jews.

"I know how many people with Hungarian ancestry live in Israel, and how many Israeli Jews live in Hungary," Gyongyosi told parliament, according to a video. "I think such a conflict makes it timely to tally up people of Jewish ancestry who live here, especially in the Hungarian parliament and the Hungarian government, who, indeed, pose a national security risk to Hungary."

On Tuesday, Gyongyosi said he was sorry for making comments which "could be misunderstood". He had been referring, he claimed, to people with dual Israeli-Hungarian citizenship.

The apology is unlikely to reassure those profoundly disturbed by his earlier comments. "Jobbik has moved from representing medieval superstition [of blood libel] to openly Nazi ideologies," wrote Slomo Koves, chief rabbi of the Unified Hungarian Jewish Congregation.