Mr. Bush said peace in the Middle East is "only possible if there is a maximum effort to end violence throughout the region, starting with Palestinian efforts to stop attacks on Israelis."
Mubarak, for his part, called for an end to forceful Israeli military tactics such as demolishing Palestinian homes and closing roads.
"Nothing can be achieved through violence or resolved by force," the Egyptian said.
"Both our countries view this situation with great alarm," President Bush said at a joint news conference with the Egyptian leader. "We're both determined to redouble our efforts to work for peace."
Mr. Bush welcomed a call by Mubarak for Israeli-Palestinian leadership talks and Saudi Arabia's proposal for normalizing relations with Israel, but said it would be hard to achieve "any kind of peace" without an end to a cycle of violence. He said he was willing to send U.S. Middle East envoy Anthony Zinni back to the region "when appropriate."
Mubarak said Israel and the Palestinians should immediately resume "full-fledged negotiations."
Mr. Bush said he and Mubarak would redouble efforts to end violence in the country, but he offered no new plans for U.S. intervention sought by Mubarak.
Mubarak said of the Israelis, "The closure of roads, the siege of towns and villages, the demolition of houses, the collective punishment that make progress more difficult should stop."
In Jerusalem, Israeli officials let it be known Sharon considers a meeting with Arafat useless while Palestinian attacks against Israelis continue. Mubarak said he would not meet with Sharon unless Arafat attended as well.
In a speech before his meeting with President Bush, Mubarak declared he was not "pro-Arafat" but said the Palestinians would be free to choose another leader after peace is achieved.
"I have no problems with the Palestinians or the Israelis," Mubarak said, as he sought to put Egypt forward as an evenhanded mediator between the two sides.
Mubarak also left no doubt about his views of Israel's continued hold on part of the West Bank and Gaza and, presumably, east Jerusalem. Without referring to Israel directly, he said "land was occupied by force" and an entire population was denied its right to nationhood.
Israel took Egypt's sprawling Sinai peninsula in the same 1967 war that it took the other lands. A 1979 peace treaty, granting Israel peace and security in exchange for the occupied territory, eventually returned the peninsula to Egypt.
Similarly, Crown Prince Abdullah of Saudi Arabia has made the price of peace Israel's withdrawal from all of the West Bank, Gaza and part of Jerusalem that Arafat wants as capital of a Palestinian state.
Mubarak said in his speech the aim of peace talks should be to "end the injustice of all the peoples" in the Middle East.
Elaborating, he said the result of the forced occupation of land had been to deny "an entire people its right to a nation."
"Occupation must end," the Egyptian president said to some 1,000 people invited by the private Council on Foreign Relations and the Middle East Institute, a research group. "Palestinians must have their rights. We want an end to the cycle of injustice."
Mubarak carried to Mr. Bush a mixed position on terrorism. He said Tuesday "the world community must work together in confronting terror," but he declined to state his position on Iraq.
It is known to be one of urging caution. Mubarak's view is that U.S. stock in the Arab world, already damaged by the Bush administration's implacable support for Israel, would sink further if Iraqis are killed in a U.S. attack.
On another sensitive subject, a senior U.S. official said the Bush administration was taking up with the Egyptians suspicions that Egypt is importing missile technology from North Korea.
Egypt has denied the allegations, but the administration does not appear to be convinced.
In Dubai, United Arab Emirates, a Saudi official said Abdullah had rejected several requests, including one from Mubarak, to meet secretly with Sharon on the proposal.
Nor would the crown prince, Saudi's de facto leader because of the illness of King Fahd, consider a meeting between lower-ranking Israelis and Saudis, according to the Saudi official, who spoke on condition of anonymity.
Abdullah "is well aware of the kingdom's standing in the Islamic and Arab worlds, and he (would) prefer to withdraw his proposal if its success depended on a Saudi-Israeli meeting," the official said.