"Mr Peres put forward his view of the situation in the Middle East, focussed on his determination to achieve a fair and comprehensive peace," Mubarak's political adviser Usama al-Baz said after the talks on Thursday.
"The meeting centred on ways of strengthening the peace process between Israel and the Arab countries and the future of the Middle East once peace is established," he said.
Peres said for his part that "we have exchanged views on how to carry out the peace process because there is a fair chance to a new road of peace (and) we don't want to miss it."
"There is a major chance," he added, saying that for the first time both the right and left in Israel had said there was no solution but two separate states for the Israelis and Palestinians.
Peres's Labour Party on Wednesday said that its leader, a former prime minister and a leading Israeli dove, was invited by Mubarak and their talks would focus on the Israeli-Palestinian conflict.
Accompanying Peres were four senior Labour officials, including the former head of the party, Amram Mitzna, and former defence minister Binyamin Ben Eliezer.
Egypt maintains contact with the Labour party and Mubarak phoned Peres earlier this month to congratulate him on his re-election as party leader.