Top US officials say their strategy in fighting the war against Iraq has been vindicated by the rapid conquest of Baghdad.
Mr Bush watched on TV as the statue fell
President Bush has not yet appeared in public since the scenes of the liberation of Baghdad, but his spokesman Ari Fleischer said that "it's an historic moment."
He said Mr Bush was heartened by "demonstration of the power of freedom" that was being seen on the streets of Baghdad, but he cautioned the US people that the fight was not yet over.
However, in a rare public appearance, the vice-president, Dick Cheney, told newspaper editors in New Orleans that "with every day, with every advance of our coalition forces, the wisdom of that plan becomes more apparent."
But officials stopped short of claiming final victory, with state department spokesman Richard Boucher saying that he would not claim there was regime change yet in Iraq.
And Donald Rumsfeld, the defence secretary, said:
"The tide is turning. The regime has been dealt a serious blow. But coalition forces will not stop until they have finished the job."
The US forces: Now seen as liberators
We are seeing history unfold, events that will shape the course of a country, the fate of the people and potentially the future of the region," he added.
Mr Cheney criticised the armchair critics of the war as "retired military officers embedded in TV studios," and said that the war was "one of the most remarkable military campaigns ever conducted."
He warned that there could be "hard fighting ahead" in Northern Iraq, but the campaign was a warning to terrorist regimes that the US had the capacity and the will to wage war on them.
Mr Cheney announced that the US would call a conference of liberated Iraqis, and exiles, in Nasiriya on Saturday as part of the process of forming an interim Iraqi authority.
US forces recently flew the Iraqi exile leader Ahmed Chalabi into that part of Iraq, but the White House later said that the meeting had been postponed, and the State Department said the venue was still undecided.
The meeting is expected to be chaired by White House special envoy Zalmay
Khalilzad, State Department assistant secretary Ryan Crocker, and a defence department official.
And Donald Rumsfeld said that the Pentagon reconstruction team led by retired General Jay Garner would fly into Baghdad as soon as the security situation allowed it.
Mr Cheney said that the key role in reconstructing Iraq had to rest with the United States, rather than the United Nations.
"We don't believe that the United Nations is equipped to play that central role. It will play a very important role, but I think the central role will reside with the coalition," he said.
And the vice-president said that the oil revenues would now belong to the Iraqi people.
"The oil revenue is not to be diverted to anything but to service the immediate and eventually the long-term needs of the
people of Iraq," he added.
Mr Cheney said that the oil fields could bring in revenues of $20bn a year, but further investment was needed as they had fallen into disrepair.
Meanwhile, in Dearborn, Michigan, where one of the largest Iraqi communities in the US is located, a crowd of 200 Iraqi demonstrated, waved US flags and honked car horns.
War on terrorism
Mr Rumsfeld listed a long series of tasks that US forces still needed to complete in Iraq.
Among the most important was finding weapons of mass destruction, investigating terror links by the regime, securing the borders and preventing leaders from leaving the country, he said.
Mr Rumsfeld again warned Syria not to provide war materials to Iraq or act as a safe haven for their leaders.
And John Bolton, the under-secretary of state for non-proliferation, warned Syria to give up its attempts to acquire weapons of mass destruction.
"We are hopeful that a number of regimes will draw the appropriate lesson from Iraq, that the pursuit of weapons of mass destruction is not in their interests," he said.