Updated

President Bush and Egyptian President Hosni Mubarak (search) gave qualified support Monday to the idea of Israeli withdrawal from some Arab areas but said it must be part of a Mideast peace agreement that would establish a Palestinian state.

Beginning an intense focus on the Middle East, Bush welcomed the Egyptian leader to his Texas ranch where talks centered on Israeli Prime Minister Arial Sharon's (search) plan for a unilateral withdrawal from the Gaza Strip (search).

Bush said he would not prejudge what Sharon would tell him at a White House meeting on Wednesday. The president referred to Sharon's plan as "rumors of such a withdrawal."

But in a joint statement released Monday evening, the two leaders said: "We believe that an Israeli withdrawal from Gaza and parts of the West Bank can, under the right conditions, and if it is within the context of the implementation of the roadmap and President Bush's vision, be a significant step forward."

Bush and Mubarak also discussed the surge of violence in Iraq. Bush said conditions have improved in recent days, referring to a tenuous truce in Fallujah, while Mubarak expressed "serious concerns about the current state of affairs, particularly in the security and the humanitarian areas."

With U.S. casualties on the rise, Bush announced he would hold a prime-time news conference Tuesday night to address Iraq. White House spokesman Scott McClellan said Bush decided to hold the 8:30 p.m. EDT session because "we're at a critical period in Iraq" and he wanted to update the American people "on where we are in Iraq right now, and where we're headed."

Like other Arab leaders, Mubarak worries that Israel's withdrawal from Gaza might be Sharon's way of holding on indefinitely to other occupied Arab land.

Just hours before flying to the United States, Sharon said Israel would seek to retain five large West Bank settlement blocs. A unilateral Israeli withdrawal from the Gaza Strip and parts of the West Bank is good for Israel's security and will strengthen large West Bank settlements, he said.

Mubarak and Bush agreed that an Israeli withdrawal from Gaza would mark a positive step if it is part of the "road map," the U.S. formula for a peace agreement and a future Palestinian state.

"I think any withdrawal from the occupied territory is very highly appreciated," Mubarak said. But he said if it is not connected with the road map, "It will not be accepted by the public opinion in the area."

Bush said: "If he were to withdraw from the Gaza, it would be a positive development."

The Gaza pullout, which includes the evacuation of all 21 settlements in the strip, is among a series of unilateral measures Sharon has proposed to separate Israelis and Palestinians in the absence of a peace agreement.

Bush offered an appeal for true peace in the entire Middle East, "not just a pause between wars."

"We also believe the future of the Middle East and the future of Iraq are closely linked," Bush said. "The people of the greater Middle East have a right to be safe, secure, prosperous and free."

But, Bush said, a Palestinian state would remain in jeopardy "if terrorists are willing to kill" in order to interrupt progress. "We can't let people blow up the process, but that's what's happening," Bush said.

"It's a very complicated problem," Mubarak said.

Violence in Iraq threatened to overshadow the Israel-Palestinian issues at Bush's talks with Mubarak.

Nearly 900 Iraqis and some 50 U.S. soldiers have died in the past week in battles between insurgents and U.S.-led coalition forces.

"It was a tough week, because there was lawlessness and gangs that were trying to take the law in their own hands," said Bush, whose national security team meeting on Monday in Crawford included Gen. John Abizaid, the top commander of U.S. forces in the Middle East, and Lt. Gen. Ricardo Sanchez over a video link from Iraq. "These were people that were trying to make a statement prior to the transfer of sovereignty that they would get to decide the fate of Iraq through violence."

Bush said U.S. troops tried to ensure innocent Iraqis were not caught up in the violence.

"We're a compassionate country that cares about the loss of innocent life and it grieves us when we see innocent life lost," he said. "However, we will defend ourselves."

He also renewed his insistence that the United States will hand over political power to Iraqis by the planned June 30 deadline. "We will transfer sovereignty," he said.

Mubarak pressed Bush to restore "Iraq's sovereignty as soon as possible" while ensuring that the emerging government "unites all Iraqis toward a common future."

"The recent efforts to increase the role of the U.N. in that process is an important step that should be further encouraged," he said.