"These terrorists are targeting the very success and freedom we are providing to the Iraqi people," Mr. Bush told reporters in the Rose Garden. "Desperate attacks on innocent civilians will not intimidate us."
Asked if he would promise to reduce the number of troops in Iraq in a year's time, the president called it a "trick question" and refused to answer.
Turning to the California wildfires, Mr. Bush expressed "my deep concerns and sympathies for those whose lives have been hurt badly by these fires."
"The federal government is working closely with the state government to provide the resources necessary to help the brave firefighters do their duty," he said.
It was the tenth solo news conference of Mr. Bush's presidency and his first since July 31.
Speaking nearly six months after he declared major combat operations to have ended in Iraq, Mr. Bush denied that he was surprised at the continuing level of violence.
"It is dangerous in Iraq because there are some who believe that we are soft, that the will of the United States can be shaken by suiciders," he said.
Still, Mr. Bush added, "The world is safer today because Saddam Hussein and the Taliban are gone ... Reconstruction is difficult and freedom still has its enemies in both of those countries."
Mr. Bush spoke on a day when a car bomb exploded Tuesday near a police station in Fallujah, 40 miles west of Baghdad, killing at least four people, one day after a series of suicide bombings in Baghdad let about three dozen dead and more than 200 wounded.
The coordinated attacks Monday came against the Red Cross headquarters in Baghdad and three police stations.
Mr. Bush was asked who was behind the recent wave of attacks.
"We're trying to determine the nature of who these people were, but I would assume that they're either or and probably both Baathists and foreign terrorists," he said.
The Baathists, those loyal to the outsed Iraqi leader, "try to create chaos and fear because they realize that a free Iraq will deny them the excessive privilege they had under Saddam Hussein," Mr. Bush said.
Turning to the Middle East, Mr. Bush said Palestinian leaders still haven't done what's needed for an independent Palestinian state to come forth.
He said he's not seeing a commitment to fight terrorists from what he calls the "old guard" of Palestinian leaders, an apparent reference to Yasser Arafat and his cohorts.
He said terror attacks are preventing the establishment of a Palestinian state, which is called for in the latest U.S.-backed peace plan.
Mr. Bush also suggested that efforts by Israel to build more settlements and a controversial security barrier in Palestinian areas were hurting the peace process.