Israel's Haaretz newspaper reported that Valter Pomar, secretary of international relations for the Workers Party (PT), described Avigdor Lieberman as "a racist and a fascist," during an interview
According to Haaretz, Pomar also said that "the Brazilian left is organizing protests" against Mr Lieberman "and against the policy he represents".
Lieberman ten-day visit to South America is intended to help block Iranian "infiltration" of the continent and expose Teheran's plans to allegedly develop nuclear weapons.
The ruling Workers Party has long been sharply critical of Israel's policies towards Palestinians and Lieberman has advocated a tough line on Israel's Arab minority.
He has suggested redrawing Israel's borders to push areas with heavy concentrations of its Arab citizens outside the country and under Palestinian jurisdiction, while requiring those who remain to sign an oath of loyalty to the Jewish state. About 20% of Israel's seven million citizens are Arabs.
A spokesperson for President Lula said Mr Pomar's words "were just his own opinion and have nothing to do with the government. In fact, they were quite rude".
Iran's ambassador to Brazil, Moshen Shaterzadeh, said on Monday that Iranian president Mahmoud Ahmadinejad would also visit Brazil.
Mr Lieberman tour will take also him to Argentina, Peru and Colombia, but he is bypassing the South American nations most closely allied with Iran, Venezuela and Bolivia.
Mercopress