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Claiming that Mr Abbas represented a partner for peace, he added: "I believe that a historic and hard-won and lasting peace is within your reach. I urge you to take it by the hand."
Mr Brown also spoke at length about how his father had instilled in him a deep admiration for the creation of the state of Israel.
He said he was looking forward to taking his own sons, John, 4, and Fraser, 2, to the country.
"I will walk them here and tell them the story of how for two thousand years, until 1948, the persistent call of the Jewish people was 'Next year in Jerusalem'. Yet for two thousand years there was not one piece of land anywhere in the world that you could call your own. For two thousand years, not one piece of land of your own to follow your faith without fear. For two thousand years you had a history but not a home."
Not even the horror of the Holocaust "could ever break the spirit of a people yearning to be free" he said.
The Prime Minister also floated the idea of forming a "peaceful civilian force", featuring men and women from all over the world, who could travel to assist in areas in need of reconstruction or assistance. The global corps - for which Mr Brown pledged a squad of "1,000 experts and professionals" from Britain - echoed calls by Sir Richard Dannatt, Head of the Army, for a special civilian reconstruction force to be developed to assist the Army in nation-building in the aftermath of any future conflict.
Mr Brown’s speech to the Knesset comes at the end of his first visit to Israel as Prime Minister, during which he also sought to add impetus to restarted peace talks with the Palestinians.
Speaking with President Abbas in Bethlehem, Mr Brown pledged a £30 million package of economic and security help for the Palestinian Authority. He said that the security wall erected by Israel was "graphic evidence of the urgent need for justice for the Palestinian people" and called on Tel Aviv to stop the spread of settlements.
"We want to see a freeze on settlements. Settlement expansion has made peace harder to achieve," the Prime Minister said.
"It erodes trust, it heightens Palestinian suffering, it makes the compromises Israel will need to make for peace more difficult."
His appeal came as a human rights group released a video of an Israeli soldier shooting a rubber bullet at a Palestinian man who had been arrested and bound during a protest against the wall Israel has built inside the West Bank to stop attacks on its territory.
Yesterday, Mr Brown laid a wreath at Yad Vashem, the Holocaust memorial in Jerusalem.
In the guest book he wrote: "Nothing prepares you for the story that is told of the atrocities that should never have happened and the truth that everyone who loves humanity should know. We must always remember so that prejudice, discrimination, racism and anti-Semitism [can] be banished from our world." Later, he visited the Church of the Nativity in Bethlehem.
Tomorrow, he will make a statement to the Commons on expected troop withdrawals from Iraq, in which almost all soldiers could leave the country within a year.
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