Mubarak said Egypt was working to "seal the crack" between Hamas and Fatah who have been fighting for control of the Palestinian government since the Islamic militant Hamas ousted its rival from power last year.
But the Egyptian leader stressed that a deal also must be brokered to secure the release of Shalit, captured by Palestinian militants 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. We are working on this line, and we hope that we reach a solution soon," Mubarak said during a joint press conference with visiting German Chancellor Angela Merkel.
Merkel was in Egypt on the first leg of her four-day Middle East tour in hope of boosting international efforts to revive the Israeli-Palestinian peace process.
Her visit comes one day after the Quartet of Mideast negotiators - the United States, United Nations, European Union and Russia - convened in Washington to discuss how to move peace talks in the region forward.
The Quartet's particular focus is on pushing forward the internationally backed "Road Map" for peace, which outlined stages for setting up a Palestinian state alongside Israel. The plan stalled almost immediately as both the Israelis and the Palestinians failed to meet their obligations.
"For me it is very important that the EU and the Mideast Quartet are helpful to the region and are not each working in our own corners, but develop a coherent strategy so that all players are working for the same goal," said Merkel, who has made the revival of Mideast peace efforts a goal of Germany's turn at the six-month rotating European Union presidency.
But the Middle East tour comes amid renewed fighting between Hamas militants and security forces loyal to the former ruling Fatah Party that has raised new alarm about a possible Palestinian civil war.
More than 100 Palestinians have been killed in internal violence since Hamas, which rejects Israel's right to exist, won parliamentary elections a year ago and wrested power from Fatah, which advocates peacemaking with Israel.
"What is happening now is a problem between the Palestinians themselves, and it is impossible for the Palestinian side to sit with the Israelis as they are still not agreeing with each other," Mubarak said.
Mubarak described his meeting with Merkel as "useful and constructive" and said the two also discussed the ongoing war in Iraq, the political crisis in Lebanon, Iran's dispute nuclear program and the conflict in Somalia and Sudan's war-ravaged Darfur region.
Merkel's tour also will take her to Saudi Arabia, the United Arab Emirates and Kuwait.