President Bush is condemning this week's suicide bombings in Baghdad and Jerusalem, saying there will be no retreat in the war on terrorism.
In his weekly radio address, President Bush said this week's attacks are further proof that terrorists have declared war on every free nation and must be defeated.
"Terrorists commit atrocities because they want the civilized world to flinch and retreat so they can impose their totalitarian vision," he said. "There will be no flinching in this war on terror, and there will be no retreat."
President Bush says progress is being made in reconstructing Iraq, but he says such improvement makes the remaining terrorists in the country "more desperate and willing to lash out" against symbols of order and hope.
"Working with Iraqis, coalition forces are on the offensive against these killers," said President Bush. "Aided by increasing flow of intelligence from ordinary Iraqis, we are stepping up raids, seizing enemy weapons, and capturing enemy leaders. The United States, the United Nations, and the civilized world will continue to stand with the people of Iraq as they reclaim their nation and their future."
Mr. Bush says murderers must not be allowed to decide the future of the Middle East.
The president says a Palestinian state will never be built on a foundation of violence.
"The hopes of that state and the security of Israel both depend on an unrelenting campaign against terror waged by all parties in the region," he said. "In the Middle East, true peace has deadly enemies. Yet America will be a consistent friend of every leader who works for peace by actively opposing violence."
Mr. Bush says by continuing acts of murder and destruction, terrorists are testing America's will.
He said, however, across the world terrorists are finding that commitment cannot be shaken.
The president pledged to continue the "war on terror until all killers are brought to justice."