He later retreated slightly after a recording of the exchange was posted on Kikar Shabbat, an ultra-Orthodox Jewish website. "I stressed several times I was not calling to take operative steps, but that this is the Rambam’s approach and that it’s the responsibility of the government, not of individuals," he said in a statement.
Nevertheless, the incendiary comments could not have been more provocatively timed. They came after Moshe Ya'alon, Israel's defence minister, ordered the detention without trial of Mordechai Meyer, 18, for extremist activities believed to include starting a fire that badly damaged the symbolic Church of Loaves and Fishes in Galilee in June.
He was one of three extremists detained after Benjamin Netanyahu's government was prompted to launch an unprecedented offensive against "Jewish terrorism" following an arson attack by suspected hardline settlers in the West Bank village of Duma last Friday that killed a one-year-old Palestinian toddler and gravely injured his parents and brother.
Head of a Jewish extremist group Meir Ettinger appears in court in Nazareth Illit (AP)
Also arrested was Meir Ettinger, grandson of the late Meir Kahane, a Jewish rabbi notorious for racist beliefs who was murdered by a Palestinian in 1990.
Mr Gopstein, Lehava's founder, is a one-time member of Mr Kahane's Kach party, which was banned because of its racist philosophy.
However, Shin Bet - Israel's domestic intelligence agency - recently concluded that there are no legal grounds for similarly outlawing Lehava, despite a request from Mr Ya'alon to consider doing so.
Two of the group's members were recently jailed for setting fire to Jerusalem's Jewish-Arab Max Rayne Hand in Hand school last November. Hebrew graffiti reading "Kahane was right" was sprayed on a wall of the school.
Mr Gopstein was arrested along with 20 other Lehava members for suspected incitement to violence last last year but has so far not been charged.
Lehava - whose name means "flame" but is also the Hebrew acronym for "prevening assimilation in the Holy Land" - regularly holds open gatherings in Jerusalem's Zion Square, where members distribute literature warning of the dangers of relationships between Jewish women and Arab men.
The group held a demonstration at which members chanted "death to the Arabs" outside a wedding between a Muslim and Jewish woman who had converted to Islam during last summer's Gaza war.
It also staged a protest against last week's gay pride march in Jerusalem, where an ultra-Orthodox Jewish man attacked six participants, leading to the death of a 16-year-old girl.