"I certainly didn't lie," he said, adding he was asked by "a newspaper" in 2016 which could not tell him where he had made the statement.
He said broadcaster Andrew Neil asked the same question in 2018 and at that point he still did not remember saying it so said he had not.
He said the speech was "from 2014, five years ago, before I was even a Member of Parliament".
Ms Barnett called the speech in which he made the remarks "impassioned" and listed the other statements, including "Zionism is the enemy of the Palestinian people."
She asked again "Why did you lie?"
Mr Burgon said: "I just explained, I didn't lie."
The encounter angered Jewish Labour Movement chair Mike Katz, who said his letter to Labour demanding an explanation from Mr Burgon received "no reply, let alone an apology and resignation".
"Guess the party leadership really wants to rebuild trust with the Jewish community," he said.
