Polish President Lech Kaczynski and a major Jewish human rights organisation have called on the Catholic Church to punish a controversial Polish priest.
Mr Rydzyk has not denied making the comments
Father Tadeusz Rydzyk is accused of an anti-Semitic outburst, and of insulting Mr Kaczynski, at a conference in April.
Fr Rydzyk says his remarks have been blown out of proportion.
The Simon Wiesenthal Centre has launched a petition calling for his dismissal, and Mr Kaczynski says there must be "consequences".
Fr Rydzyk controls the influential Radio Maryja radio station, which correspondents say helped Mr Kaczynski's Law and Justice party win parliamentary and presidential elections in 2005.
In tapes released by the weekly magazine Wprost, a voice alleged to be Fr Rydzyk's is heard accusing Mr Kaczynski of being in the pocket of Poland's Jewish community.
"You know what this is about: Poland giving [the Jews] $65bn.
"They will come to you and say, 'Give me your coat! Take off your trousers! Give me your shoes!'" Fr Rydzyk said, according to Wprost.
The speaker is also heard calling President Kaczynski a liar, and his wife Maria a "witch" because of her support for limited abortion rights, which he compares to euthanasia.
"The first lady with this euthanasia... You witch, I'll let you have it. If you want to kill people, do it to yourself first," he says on the tape.
Fr Rydzyk has accused Wprost of provocation, but has not denied making the comments.
The Simon Wiesenthal Centre, which campaigns against anti-Semitism and extremism, said Fr Rydzyk was guilty of "leveraging Jew-hatred to promote his extremist agenda".
President Kaczynski said that if the tape was genuine, the insult must have consequences.
His brother, Prime Minister Jaroslaw Kaczynski, said it was a "serious problem" which Fr Rydzyk's superiors in the Church needed to address.