But after the worst month for US forces in Iraq, Bush insisted the deaths of 130-plus US troops in April will not be in vain.
The US leader is confronting growing public disapproval of his action in Iraq and critics have been focusing on a speech he made on 1 May last year on the USS Abraham Lincoln.
With a banner in the background declaring "Mission Accomplished", Bush said that "major combat operations" were over in Iraq after the fall of Iraqi leader Saddam Hussein.
Twelve months on, the president justified his comments in his weekly radio address saying he had been welcoming the success of "one of the swiftest, most successful and humane campaigns in military history".
Without mentioning the heavy toll suffered in April, which was more than the 109 troops killed during the invasion, Bush said that US forces are "sacrificing greatly".
But the president also admitted: "On the ground in Iraq, we have serious and continuing challenges."
Top administration officials have admitted they did not anticipate the degree of unrest that has blown up in recent weeks, particularly in the cities of Falluja and Najaf.
"Our coalition supports the efforts of local Iraqis to negotiate the disarmament of the radicals in Falluja. We've also made it clear that militias in Najaf and elsewhere must disarm or face grave consequences.
"We will not be intimidated or diverted"
"American and coalition forces are in place, and we are prepared to enforce order in Iraq."
He said the transfer of power, which is being worked out by UN special envoy Al-Akhdar al-Ibrahimi, was the second element of the US strategy.
But he warned: "As the transfer of sovereignty approaches on 30 June, we are likely to see more violence from groups opposed to freedom." Bush said the US would "ensure an atmosphere of security" for the handover of limited power on that day.
"We will not be intimidated or diverted. On 1 July, and beyond, our reconstruction and military commitment will continue," Bush said.