Sharm el-Sheik, Egypt ? Vice President Dick Cheney said Wednesday that Israel and the Palestinians share the burden of ending Middle East bloodshed. Egyptian President Hosni Mubarak met with Cheney and promised to apply pressure, too.

At a news conference with Cheney at this Red Sea resort, Mubarak also addressed another difficult Mideast issue, saying he believes Iraq’s Saddam Hussein is close to agreeing to allow the return of U.N. weapons inspectors.

One of Cheney’s missions on his trip to the region  to make a case for widening the war on terrorism to include Iraq  has been overshadowed by the spiraling loss of life in the Israeli-Palestinian conflict.

“The United States will do all it can to end the tragic violence between Palestinians and Israelis and to resume a serious negotiating process,” Cheney said.

The Bush administration, which has demanded that Palestinian leader Yasser Arafat do more to end the violence, has lately been more openly critical of Israeli Prime Minister Ariel Sharon.

Asked whether he believed the burden for restoring peace had shifted to Sharon given this week’s Israeli offensive in the West Bank and Gaza, Cheney said: “I think the burden is on both parties to bring an end to the violence.”

Mubarak cited “great concern” over what he called “the current deteriorating situation in the Middle East.”

He said he and Cheney agreed to make “extensive efforts” to try to put into place an initiative by CIA Director George Tenet and former U.S. Senate Majority Leader George Mitchell.

The plan calls for an end to violence, to be followed by measures to restore mutual confidence and a return to negotiations for a political settlement.

Cheney praised Tuesday’s United Nations resolution calling for the first time for establishment of a Palestinian state. “The president’s made clear that the U.S. vision for that part of the world includes a Palestinian homeland as well,” he said.

The vice president is on a tour of nine Arab states, Israel and Turkey.

Earlier Wednesday, Cheney visited a multinational outpost set up here to help monitor enforcement of the 1979 peace agreement between Israel and Egypt.

Some 865 Americans are part of the 1,836-member force of observers patrolling the desert between Egypt and Israel. Defense Secretary Donald Rumsfeld is trying to sharply cut back the U.S. participation, a fact Cheney did not bring up.

Mubarak voiced public opposition to any U.S. plan to topple Saddam in Iraq, just as Jordan’s King Abdullah II had during Cheney’s visit to Jordan the day before.

“It is of vital importance to maintain the sovereignty and territorial integrity of Iraq. This is a must for preserving regional stability,” Mubarak said.

He suggested that Saddam be given a final chance to comply with U.N. resolutions, including those demanding the return of U.N. weapons inspectors.

“And I think, as far as my knowledge is that he is going to accept the inspectors,” Mubarak said, without elaboration.