The United States and British governments expressed satisfaction over the apparent end of the era of Saddam Hussein, but hesitated to claim victory and warned of further combat before the regime was finished.
"We are still in the midst of a shooting war, and men and women are still in harm's way. The war is not over. There remain a lot of dangers ahead," said White House spokesman, Mr Ari Fleischer.
However, the regime's collapse was acknowledged by the Iraqi ambassador to the UN, Mr Mohammed al-Douri, who said outside his New York residence that the "game is over, the war is over. My hope now is for peace."
Mr Bush watched on television in the White House as Iraqis attacked the statue of Saddam Hussein in Baghdad, and returned after a meeting with the president of Slovakia to see a recording of US troops finishing the job. The president saw it as an "historic moment" with "heartening signs of military progress and mankind's taste for freedom," Mr Fleischer said.
Members of the large Iraqi community living in Deerborne, Michigan, took to the streets with American and Iraqi flags to celebrate after witnessing the statue of Saddam being pulled down.
With the focus in the coming days turning to the establishment of a new administration in Iraq, US VicePresident Mr Dick Cheney, bluntly said in New Orleans, "We don't believe that the United Nations is equipped to play that central role."
He also warned the war has sent a clear message that the US had the capacity and the will to wage war on terrorism and win decisively.
The British Prime Minister, Mr Tony Blair, joined Downing Street staff to watch the TV images and his spokesman said the whole of No 10 was "delighted" at the scenes from the Iraqi capital. In the Commons, Mr Blair warned: "There are still some very difficult things to do, and as we speak there is still intense resistance."
The US Defence Secretary, Mr Donald Rumsfeld, said: "We had a good day today but it's not over yet," and added that "the faces of the liberated Iraqis, the free Iraqis," showed that "the mood in the country is in fact tipping."
US officials shed no further light on the fate of Saddam Hussein, despite claims he had been killed in a US air strike on Monday.