But Mr Kasidiaris, who had served in the Greek military's special forces, hit Ms Kanelli around the face three times. A public prosecutor ordered his immediate arrest.
Mr Kasidiaris was elected to Parliament in the country's recent inconclusive polls. Deputies from all seven parties that won parliament seats in the May 6 polls had been invited on the show.
"The government condemns in the most categorical way the attack by Golden Dawn spokesman Ilias Kasidiaris against Liana Kanelli and Rena Dourou," government spokesman Dimitris Tsiodras said. "This attack is an attack against every democratic citizen."
Mr Tsiodras called on Golden Dawn to condemn its member's actions.
Golden Dawn, which vehemently denies the neo-Nazi label, has been accused of being behind violent attacks against immigrants.
The party won nearly 7 percent of the vote on May 6, giving it 21 seats in the 300-member Parliament. It was a radical increase from its showing in the previous elections in 2009, when the party had won just 0.31 percent of the vote.
Greeks reeling from two years of austerity amid their country's vicious financial crisis punished the two formerly main parties, the conservative New Democracy and socialist PASOK at the polls, turning instead to radical smaller parties to the right and left of the political spectrum.
The 300 deputies took up their seats for a day last month before parliament was dissolved and new elections called as no party had won enough votes to form a government on its own, and negotiations for a coalition government collapsed after 10 days.