"Israeli and Palestinian children dream of two goals," Peres told the visitors in remarks broadcast on public radio. "Scoring the winning goal at Camp Nou, and the great goal of peace."
The players and staff arrived on yesterday on their "Peace Tour" and travelled to the West Bank city of Bethlehem to visit the Church of the Nativity, where Jesus is believed to have been born.
After meeting Palestinian president Mahmud Abbas at his Ramallah headquarters they held a football clinic near the southern West Bank town of Dura.
After a reception at Peres's Jerusalem residence, the team was due later to give a coaching session to Israeli youngsters in Tel Aviv.
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Peres, who turned 90 on Friday, is to deliver the opening kick.
"Barca is more than just a club," he said at the reception.
"You became each of you messengers of peace."
"Sport, and football in particular, breaks down barriers," he added. "In football there are no victims but always hope for the next match."
The training sessions are organised by the Peres Centre for Peace as well as the Israeli and Palestinian football federations.
It was a decision which sparked calls for a boycott of the Catalan club.