The farmer, from Biella in northern Italy, made the comments during an interview with the daily newspaper, La Repubblica.
"It's curious and is something I need to figure out,” he added.
Rothschilds is an international banking dynasty that was founded by Mayer Amschel Rothschild in Frankfurt’s Jewish ghetto in the 18th century.
Renzo Gattegna, the president of the Union of Italian Jewish Communities, said the remarks were “delusional”.
Gattegna told Il Sole 24 that the claims “give a sense of unease that becomes even deeper, and recalls, without shame, a period of history characterized by death, violence and denial of the most basic rights.”
Zunino's comments come just days after it was reported that football rivals were using stickers of Holocaust victim Anne Frank, something Rabbi Barbara Aiello told The Local was symptomatic of a rise in anti-Semitism across Europe. READ MORE HERE: Football fans use Anne Frank in anti-Jew attack
In his interview, Zunino also said anti-austerity protesters “want the government to resign” and are calling for the “sovereignty of Italy”.
He also heaped praise on Beppe Grillo, the leader of the anti-establishment 5-Star Movement, and Hungarian Prime Minister Viktor Orbàn, whose right-wing government has downplayed rising anti-Semitism in the country.
The Pitchfork (Forconi) movement started in Sicily last week among farmers incensed by rising taxes and soon spread to truck drivers, store owners and craftsmen who are increasingly frustrated with reforms demanded by cost-conscious Rome.
On Thursday, protesters blocked main roads between Italy and France. READ MORE HERE. Protesters block Italy-France border
The protests have at times been violent, prompting Italy’s deputy prime minister, Angelino Alfano, to say on Thursday that the rallies could attract “violent groups”.
“While protest is acceptable in a democracy, violence will not be tolerated”, he warned.