Mubarak openly disagreed with Peres' one-track approach, saying the Saudi initiative is not "open for negotiations."
Under the terms of the Saudi plan, Israel would get Arab recognition in return for withdrawing from occupied Arab lands.
Israel's apparent openness to the Arab plan is in contrast to it's rejection of the Saudi project when it was unveiled in the Lebanese capital Beirut in March 2002.
US-baked peace talks between Israel and the Palestinians have stalled in recent weeks, pending the formation of a new Israeli government.
Tzipi Livni, Israel's foreign minister, is trying to set up a coalition government after Ehud Olmert resigned from the prime ministerial post last month amid corruption allegations against him.
The Egyptian president has promised that Cairo will boost effort to secure the release of an Israeli soldier captured in Gaza more than two years ago, Peres said.
Mubarak "promised me to increase the efforts to release Gilad Shalit that would affect not only one family but the entire people of the region," Peres said.
"I hope the efforts to bring about his release will be increased and yield results," he said.
Mubarak "confirmed Egypt's efforts to bringing positions closer that would lead to the agreement for the release of Shalit and Palestinian prisoners."
Egyptian mediation between Israel and Hamas, a Palestinian group listed by Israel and the US as a terrorist group, has been crucial in recent months.
While Israel is looking for Shalit's safe return, Hamas has called for the release of about 1,400 Palestinian prisoners from Israeli jails.
Mubarak said that the Egyptian-brokered prisoner exchange talks had not failed.
"We have not failed ... The Israeli side knows perfectly well what Egypt is doing in regards to Shalit," he said.
Hamas has had de facto control of Gaza since June 2007, when forces loyal to it defeated forces loyal to Mahmoud Abbas, the Palestinian president and head of Fatah.
Israel and Hamas are currently observing a six-month truce brokered by Cairo in June.
Israel and the Palestinians relaunched peace talks last November at a US-hosted conference with the goal of reaching a deal by the end of 2008.
However, most analysts believe that a full deal by the end of the year is highly unlikely.