The world leaders also indicated they thought conditions may be more favorable now than in previous years to advance Arab-Israeli peace efforts, but tempered their remarks by noting the complications that accompany the process.
"If all sides are willing to move off of the rut that we're in currently, then I think there is a extraordinary opportunity to make real progress. But we're not there yet," Obama said. "I'm encouraged by some of the things I'm seeing on the ground."
Mubarak said he has told Israeli leaders that a temporary solution and "temporary borders" won't work.
"This issue has been ongoing 60 years. And we cannot afford wasting more time, because violence will increase, and violence has increased," the Egyptian leader said. "The level of violence is now much more than it was 10 years ago. Therefore, we need to find, to move to the final status solution and level."
During the media availability after their meeting, Obama and Mubarak said they also discussed nuclear proliferation and Iran, the situation in Iraq and Somalia.
Mubarak also said they talked about human rights and democracy, for which he has been criticized by human rights groups. He said they discussed reform inside of Egypt in a frank but friendly manner.
"I told to President Obama very frankly and very friendly that I have entered into the elections based on a platform that included reforms," Mubarak said, "and therefore we have started to implement some of it and we still have two more years to implement it."
Notable deaths of 2014 [PHOTOS]