Instead, Mr Sharon expressed appreciation for the "deep friendship" of the United States in a telephone conversation on Friday with US Secretary of State Colin Powell, the Israeli government press office said.
Meanwhile, about 1,000 troops are on their way to Uzbekistan in the first major deployment of ground forces in the campaign against terrorism, US officials said.
In other developments:
Mr Sharon's remark about appeasement on Thursday was his strongest criticism yet of the United States, Israel's closest ally.
It followed Mr Bush's endorsement earlier in the week of a Palestinian state.
He compared the treatment of Israel to events leading up to World War II, when Britain and France stood by while Nazi Germany dismembered Czechoslovakia.
"I call on the Western democracies, and primarily the Free World, the United States, do not repeat the dreadful mistake of 1938 when Europe sacrificed Czechoslovakia. Do not try to appease the Arabs at our expense," Mr Sharon said.
One of Mr Sharon's aides quickly said that the prime minister had not meant to imply that the United States was acting in a "dishonourable way".
But that is exactly how Mr Sharon's use of the emotive term "appeasement" seems to have been understood in Washington, analysts said.
Ground troops deployment
Troops from the US Army's 10th Mountain Division heading to Uzbekistan can use only one airbase - and only for search and rescue, and humanitarian missions.
Uzbek President Islam Karimov has ruled out the launch of ground or air attacks from Uzbekistan and said special forces would not be allowed into the country.
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The US has already assembled 30,000 other military personnel, 350 aircraft and two aircraft carriers in the region, with two more battle groups on the way.
A UK aircraft carrier is also in the area, taking part in major military exercises in Oman and available for action.
US Defence Secretary Donald Rumsfeld has been in Turkey, the final destination of his alliance-building tour of Middle Eastern and central Asian counties.
As the only Islamic country in Nato, Turkey occupies a potentially crucial role as a bridge between the US and Muslim states which have signed up to the coalition.
Calling Turkey a valiant and close friend, Mr Rumsfeld placed great emphasis on the close relationship that the United States and Turkey enjoys.
But he revealed nothing about the content of his conversation with the Turkish Prime Minister Bulent Ecevit, and played down any specific military issues that may have been discussed.
UK Prime Minister Tony Blair is also rallying support for the fight against global terrorism. He has arrived in India following a visit to Pakistan, where he offered financial assistance and increased defence cooperation in return for Islamabad's support for the international coalition against terrorism.
The BBC's Frances Harrison in Delhi says Mr Blair will now reassure India that Pakistan is not being unduly rewarded for its co-operation.
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