He threatened to target radical groups anywhere in the world to defeat "terror".
In a hard-hitting weekly radio address, Bush emphasized his campaign against "terror" was global and that no "terror outfits" would be spared.
"Terrorists commit atrocities because they want the civilised world to flinch and retreat so they can impose their totalitarian vision," he said.
"From Afghanistan to Iraq, to the Philippines and elsewhere, we are waging a campaign against the terrorists and their allies, wherever they gather, wherever they plan, and wherever they act," Bush said.
"The terrorists have declared war ... Their goals are clear. They want more governments to resemble the oppressive Taliban that once ruled Afghanistan"
"This campaign requires sacrifice, determination and resolve, and we will see through. Iraq is an essential front in this war," the president added.
Bush's address focussed on last week's bomb attacks on the UN headquarters in Baghdad and a Jerusalem bus.
"These two bombings reveal, once again, the nature of the terrorists and why they must be defeated," Bush said.
The US president however offered no comments on Israel's assassination of Ismail Abu Shanab, a senior leader of the Palestinian resistance group, Hamas.
"The terrorists have declared war on every free nation and all our citizens. Their goals are clear. They want more governments to resemble the oppressive Taliban that once ruled Afghanistan," he said.
Claims of progress
Bush claimed progress was being made by the US-led coalition in Iraq to rebuild a stable country, making the "remaining terrorists even more desperate and willing to lash out against symbols of order and hope, like coalition forces and UN personnel."
But he said that "the world will not be intimidated" in Iraq or elsewhere.
Bush said hopes for setting up a Palestinian state and establishing security for Israel "depended on an unrelenting campaign against terror waged by all parties in the region".