Orban told Parliament Monday he has instructed Minister of Interior Sandor Pinter to "ensure that it would be impossible to organize events of a political nature that may violate the marchers' human dignity" during the event.
The annual Holocaust Memorial Day event is planned for April 21 in Budapest, where it is expected tens of thousands of marchers will mark the slayings of at least 5 million Jews at the hands of the Nazis during World War II.
But last week the National-Hearted Motorcyclists posted on its Facebook page it intended to stage a counter-parade with the theme "Give Me Gas," which the Hungarian Jewish organization Mazsihisz interpreted as an offensive reference to the more than 400,000 Jews killed by poison gas at the Auschwitz death camp.
Socialist Member of Parliament Pal Steiner described the biker group as an "openly anti-Semitic organization" that was bent on staging a crude provocation to sully the memories of the concentration camp victims.
Orban, whose government has come under fire from European critics for supporting constitutional changes deemed to be anti-democratic, agreed with Steiner in Monday's speech, saying the biker group's "gas" reference was "highly distasteful."
"I categorically reject all such behavior," he said, adding that "all attempts to disregard and even purposefully violate the dignity, history and pride of certain ethnic groups while insulting human dignity are not just performed in poor taste, but are deeply hurtful and contrary to the spirit of the Constitution."
Pinter issued a statement promising the Budapest police force would ban the motorcyclists' demonstration "using all legislative means, since the time and route of the event as well as its provocative slogan offend every good-minded person."
Orban's conservative Fidesz party also condemned the biker group. Antal Rogan, its Parliamentary leader, said Sunday that any organization that times a demonstration to coincide with the March of the Living is "obviously motivated by provocative purposes."
As a politician and a participant of the March of the Living, Rogan "deeply condemns this discreditable behavior," the government said in a statement.
The Jewish group Mazsihisz said the motorcyclists plan to ride through Budapest's historic Jewish Quarter and past its Dohany Street Great Synagogue, which also houses the Hungarian Jewish Museum.
Calling the "Give Me Gas" slogan "a call to repeat the atrocities" of the Holocaust, Mazsihisz said the planned parade was an "intolerable, shameful attack."
Marton Gyongyosi, a member of the radical nationalist Jobbik Party, last year called for a list of Jewish lawmakers and government members to be published, claiming they represented a security risk, the MTI news agency reported.
Gyongyosi later changed his request to listing lawmakers holding dual Israeli-Hungarian citizenship -- a request Orban said Tuesday is causing "justified" fears among Jews and other minorities they could be used as scapegoats.