The rally outside Budapest's parliament brought together leaders from governing and opposition parties in an unprecedented show of unity in the country's deeply divided political scene.
"We cannot allow things which belong to the darkest pages of history books to repeat themselves," Antal Rogan, head of the ruling Fidesz party's parliamentary group, told demonstrators who waved national flags and demanded the resignation of Jobbik MP Marton Gyongyosi.
On Monday Gyongyosi, one of Jobbik's 44 lawmakers in the 386-seat parliament, said after a debate on fighting in the Gaza Strip it would be "timely" to tally up people of Jewish ancestry in Hungary who posed a national security risk.
He later apologised and said his remarks had been misunderstood, adding that he was referring only to Hungarians with Israeli passports in the government and parliament. But he said he would not resign.
"We do not want to live together with such malicious racist comments which we heard from Marton Gyongyosi, lawmaker of Jobbik, on Monday in parliament," Rogan said.
Former prime minister Gordon Bajnai of the centrist Egyutt (Together) 2014 movement said Gyongyosi's remarks revealed the true nature of Jobbik and parties should join forces against the far right.
"If we want a new era of normality in politics in Hungary then this is the number one moral order: one must team up with everyone against the Nazis, but must not team up with the Nazis not even for power," Bajnai told the rally.
Jobbik was registered as a party in 2003 and won increasing influence from 2006 onwards. In 2010 it became the third-biggest party in parliament on a campaign vilifying the Roma minority and attracting voters frustrated by a deepening economic crisis.
The party has retained support in the recession-hit central European country and some analysts said it could hold the balance of power between centre-right Fidesz and the left-wing opposition in the next elections in 2014.
Attila Mesterhazy, leader of the biggest opposition party, the Socialists, said "fascism is a virus and Jobbik is the one spreading this virus". He called on Prime Minister Viktor Orban to speak up in parliament on Monday to condemn Jobbik.
JOBBIK DISMISSES "ALARMISM"
Jobbik dismissed the protest as "political alarmism" in a statement on Sunday, adding that its opponents' comments reflected desperation over the rise of the party's support.
The government condemned Gyongyosi's remarks in a statement on Tuesday, pledging to do "everything" to suppress extremist, racist and anti-Semitic voices.
The protesters, who gathered in wintry temperatures, demanded immediate action against the far right and welcomed the rare manifestation of unity from politicians at the rally.
"I have come because eight members of my family were taken away (by the Nazis) and only four returned home," said Andor Freud, 76.
"Jobbik has crossed many boundaries, they should not have a place in parliament."
Businessman Gyorgy Sarkozy, 43, said: "It's very important to be here in person, all of us, to protest against what's happening in Hungary now. This is the shame of the world, this fascist movement.
"Perhaps now we will see such joining of forces which will not only restrain their (Jobbik's) rhetoric but also this whole Nazi party. This is a Nazi party."
About 500,000 to 600,000 Hungarian Jews were killed in the Holocaust, according to a memorial centre in Budapest. Some survivors reached Israel. Some 100,000 Jews now live in Hungary.
