"He [Moussa] sees a window of opportunity basically this year," Merkel said after talks with Moussa.
In Riyadh, Merkel met King Abdullah for more than an hour for talks that were described by officials in the German delegation as taking place in a "good atmosphere".
Like President Mubarak, the Saudi king has worked to mediate between Hamas and Fatah, locked in fighting for control of the Palestinian government since Hamas ousted its rival from power last year.
"It is pitiful to witness the bloody scenes in Gaza between the brothers"
Mubarak, speaking on Saturday at a joint press conference with Merkel, said Egypt was working to "seal the crack" between the two sides.
But Mubarak stressed that a deal also must be brokered to secure the release of Israeli Corporal Gilad Shalit, who was captured by Palestinian fighters in June.
Egypt has been trying to negotiate his release in exchange for Palestinians held in Israeli prisons.
"It all depends on the soldier that was detained by the Palestinians, and at the same time the Palestinians are demanding the release of their detainees," Mubarak said.
Moussa, right, spoke of the need to act
quickly for peace progress to be made [AFP]
"We are working on this line, and we hope that we reach a solution soon." King Abdullah and Merkel also discussed other regional issues, including Lebanon and Iran.
The Saudi king reiterated concerns over Tehran's nuclear programme, the German officials said, speaking on condition of anonymity because they were not authorised to talk to media.
Merkel, who has made the revival of Middle East peace efforts a goal of Germany's turn at the six-month rotating European Union presidency, is on a four-day Middle East tour.
She also will visit the United Arab Emirates and Kuwait.