Amman announced that it needed "time to clarify the US position" on the Middle East peace process on Tuesday.
The snub comes just after Bush broke with long-standing American policy and acknowledged Israel would keep many of its illegal settlements in the West Bank.
The unilateral announcement was made without any reference to the "quartet" of bodies that created the "roadmap" Middle East peace process - the UN, EU and Russian federation.
"The reason behind cancelling the trip is clear as Bush's backing of the Sharon plan made the king's visit embarrassing and meaningless," Jordanian political analysts Jamil al-Nimri told Aljazeera.net
"Jordan was hoping to make the disengagement plan part of the 'road map' and not eradicate the peace initiative completely by legalising settlements and scrapping the right of return," added al-Nimri who writes for al-Arab al-Yawm daily.
"The decision was logical and very brave."
But al-Nimri does not see this decision as affecting the overall political and economical relationship between the two countries.
"Jordan wants to have the right to disagree politically with the US without this affecting their firm relationship especially the economic one."
For its part, the White House played down the king's decision.
"We understand that there are some domestic issues involved
here and we respect King Abd Allah's decision to postpone (the meeting) for a couple of weeks," White House spokesman Scott McClellan told reporters aboard Air Force One.
King Abd Allah's move also follows the killing of Dr al-Rantisi on Saturday in Gaza.
Political commentators suggest the monarch would damage his image if seen walking around US corridors of power at a time when Israel is enjoying Washington's complete backing.
A future meeting has tentatively been rescheduled for the first week of May.
Nasir al-Kidwa asks UN to condemn
Israel's policy of political killings
A vote is expected in the UN Security Council on Tuesday after Arab states submitted a draft resolution calling for Israel to end "extra-judicial" executions.
Palestinian representative Nasir al-Kidwa said assassinations were the latest in a long series of war crimes and the Security Council's failure to condemn Israel had encouraged it to continue.
But Israeli envoy Dan Gillerman called al-Rantisi a "radical terrorist leader" and he defended the killing, saying there had been no viable means of arresting the Hamas leader.
Three weeks ago, the US vetoed a resolution condemning Israel for killing al-Rantisi's wheel chair-bound predecessor, Shaikh Yasin.
Most political analysts expect any similar resolution will also be vetoed by America.