"I told him it cannot be that at the beginning of the 21st Century there is a state which says it is going to destroy the Jewish state, there is no aggressive voice being heard condemning this."
Israel's prime minister said he was pleased with the Pope's response: "He said that he condemns all instances of anti-Semitism and hate against the state of Israel - against humanity as a whole, but in this case against Israel."
Mr Netanyahu reportedly added that Israel wanted peace with the Palestinians but "only the kind of peace that brings security".
"We don't want to dominate another people, but we also don't want a terror state backed by Iran to rise alongside us and jeopardize Israel's safety," he was quoted as saying by the Israeli newspaper Haaretz.
Mr Netanyahu's election this year was ill-received in the Arab world because of his hard-line views, including his opposition to returning land captured in wars.
Mr Netanyahu is due in Washington on 18 May for what are being seen as crucial talks with President Barack Obama.
In Bethlehem on Wednesday, the Pope delivered what correspondents say was one of his strongest expressions of support for the Palestinians, offering his backing for Palestinians' right to a "homeland".
The Pope celebrates Mass in Nazareth
He told Palestinian refugees his heart went out to families divided by detention and restrictions on freedom of movement, a reference to Israeli military control of the West Bank.
"It is understandable that you often feel frustrated," the pontiff said.
"Your legitimate aspirations for permanent homes, for an independent Palestinian state, remain unfulfilled."
In his homily at the open-air Mass, the Pope preached against prejudice and hatred "which kills men's souls before it kills their bodies".
At least 40,000 Christians, among them many Arabs, attended the service in the northern Israeli town.
Neither the oppressive morning heat nor heavy-handed security measures could stifle the enthusiasm of the faithful, the BBC's Katya Adler reports.
The Pope focussed on conservative family values, saying: "[Through] the example of Mary, Joseph and Jesus we come to appreciate even more fully the sacredness of the family which in God's plan is based on the lifelong fidelity of a man and a woman."
The traditional tone came in stark contrast to some of the Pope's speeches this week where he openly mixed prayer with politics, our correspondent says.
His attempts to smooth his strained relations with the Muslim and the Jewish communities may not have been entirely successfully but it leaves behind an impression of a player on the world stage, she adds.
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