Mubarak described talks with Hamas as "positive" but said he warned leaders of the group against holding on to their "extreme positions," urging them to pursue a responsible policy.
In compliance with Cairo's demands Israel froze a planned incursion into the northern Gaza Strip on Thursday night to give Egyptian mediators more time to secure the release of Corporal Gilad Shalit.
Shalit was kidnapped in an attack on an Israel Defense Forces' post near Gaza on Sunday. Two soldiers were killed in the attack.
Al-Ahram reported that in a conversation by phone with Prime Minister Ehud Olmert, Mubarak urged that Israel act with restraint, and warned the Israeli leader that military action in Gaza is likely to claim the lives of innocent civilians, which in turn will fuel Palestinian groups to seek revenge.
Mubarak also held talks with Palestinian President Mahmoud Abbas, Syrian President Bashar Assad and French President Jacques Chirac, the newspaper reported.