The Texan talks start a week of Mid-East diplomacy in the US
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The US and Egyptian presidents have welcomed an Israeli plan to withdraw from Gaza but said the timetable to create a Palestinian state must stand.
After private talks, George W Bush said the move would be "positive" and Hosni Mubarak said it would be "appreciated".
Israeli Prime Minister Ariel Sharon - scheduled for a meeting with Mr Bush this week - wants a unilateral pullout of settlers from the Gaza Strip.
Mr Bush added that the Iraqi situation was improving after a "tough week".
Following his private meeting at the Crawford ranch, President Mubarak said that any Israeli withdrawal was "very highly appreciated".
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We both are in agreement that if Israel makes a
decision to withdraw, it doesn't replace the roadmap
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Mr Bush added that both he and Mr Mubarak were "in agreement that if Israel makes a decision to withdraw, it doesn't replace the roadmap", referring to the US-sponsored
Mid-East peace plan which foresees an eventual Palestinian state.
Monday's talks in Texas are part of a diplomatic round which will see Mr Bush meeting Israeli Prime Minister Ariel Sharon on Wednesday and UK Prime Minister Tony Blair on Friday.
Egypt's role
Israel - and the US - would like Egypt to take responsibility for border security in the southern Gaza Strip after a withdrawal.
Netzarim is among the most heavily guarded settlements
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Israel says Palestinians smuggle weapons into Gaza from Egypt, via tunnels.
The fear is that an Israeli withdrawal from Gaza could create a new centre of instability in the Middle East,
the BBC's Jon Leyne reports from Crawford.
Egypt has indicated that it is willing to police its border with Gaza, but does not want responsibility for security within Gaza itself.
Egypt is the second-largest recipient of US aid - behind Israel - and Mr Mubarak normally visits the US once a year.
He stayed away last year in protest against the US-led invasion of Iraq and on Monday he called on Mr Bush to address "serious concerns" over security and the "humanitarian area" in Iraq and to restore Iraqi sovereignty speedily.
"The situation in Iraq has improved," Mr Bush replied.
"But... it was a tough week because there was lawlessness and gangs that were trying to take the law in their own hands."
"You just can't let, you know, a small percentage of the Iraqi people decide the fate of everybody and that's what you're seeing," he added.
Sharon's plan
Prime Minister Sharon is due to present his unilateral "disengagement plan" to President Bush at the White House.
He hopes to secure Washington's support for the plan, which will also involve the evacuation of four settlements in the northern West Bank.
There are 7,500 Jewish settlers living in enclaves alongside 1.3 million Palestinians in the Gaza Strip.
Mr Sharon's Likud Party has set 29 April as the date for a vote on the controversial Gaza disengagement plan by 200,000 Likud members. It will be followed within days by votes in the cabinet and parliament.