Mr Arafat and Mr Qurei have already had their disagreements
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Palestinian officials say Yasser Arafat has asked Prime Minister Ahmed Qurei to form a new government.
Palestinian Foreign Minister Nabil Shaath said Mr Qurei had agreed to stay on after the one-month term of his emergency cabinet expires next Tuesday.
Meanwhile, President Bush warned Palestinian leaders there could be no peace if they failed to tackle "terror".
The US president did not name Mr Qurei or Mr Arafat but said the "old guard" was not showing the same commitment as Mr Qurei's predecessor as prime minister, Mahmoud Abbas.
Uncertainty
Mr Shaath told reporters that the new government should be ready by next week and would be presented to the Palestinian parliament for approval.
He was speaking after a central committee meeting of Mr Arafat's Fatah organisation in the West Bank town of Ramallah.
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I do not see the same commitment to fight terror from the [Palestinian] old
guard
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Correspondents say there had been uncertainty over whether Mr Qurei would agree to continue as prime minister, following arguments with Mr Arafat about control of the Palestinian security forces.
Mr Qurei was sworn in by Mr Arafat as the head of an interim emergency cabinet on 7 October.
But just two days later, he threatened to resign after a row that blocked parliamentary ratification of the cabinet line-up.
His predecessor, Mahmoud Abbas, quit in September as the first Palestinian prime minister, barely five months into the job, after a power struggle with Mr Arafat.
Bush warning
US President George W Bush warned on Tuesday that what he called the Palestinian "old guard's" failure to fight terror was hampering peace efforts.
Referring to Mahmoud Abbas and his rift with Yasser Arafat, Mr Bush said the former prime minister was "eased out of power".
"And I do not see the same commitment to fight terror from the old
guard," he added.
But Mr Bush said he remained committed to a "two-state solution... a Palestinian state living side by side with Israel".