Janos Martonyi also denied suggestions that his country was lenient with neo-Nazis and other right-wing extremists, telling reporters "Hungary does not put up with" actions by such groups and individuals.
"Hungary has the strongest laws against such manifestations," he said after meeting in Vienna with Austrian Foreign Minister Michael Spindelegger.
Martonyi's comments reflect Hungary's attempts to deal with the fallout from the remarks by Marton Gyongyosi of the far-right Jobbik party, which generated headlines across Europe and outraged human rights activists.
Gyongyosi told the legislature last week that it was time "to assess ... how many people of Jewish origin there are here, and especially in the Hungarian parliament and the Hungarian government, who represent a certain national security risk."
Gyongyosi later apologized to "our Jewish compatriots" for his statement, but added that Hungary, a nation of about 10 million people, needs to be wary of "Zionist Israel and those serving it also from here."
Some 550,000 Hungarian Jews were killed in the Holocaust. Hungary's Jewish population is now estimated at 100,000.
Martonyi's center-right Fidesz party, the main group in Hungary's ruling coalition government, criticized the remarks along with all other parties in parliament.
On Sunday, senior Fidesz politician Antal Rogan told an anti-Jobbik crowd estimated at 10,000 by Hungarian media that he would take his two sons to the Auschwitz concentration camp in Poland, where it is estimated that one-third of the Nazis' victims were Hungarian.
The controversy has strengthened the platform of opposition politicians and human rights activists who accuse Fidesz of not doing enough to combat strong anti-Jewish and anti-Roma sentiment in Hungary—something Fidesz denies.
Martonyi said that Fidesz has repeatedly ruled out "any political or other cooperation with Jobbik," adding he expected unspecified political and legal consequences for Gyongyosi because of his comments.