The suicide bombings in Baghdad Monday killed about three-dozen people and caused foreign organizations to weigh their role in the insurgency-plagued nation. It was the bloodiest day in the Iraqi capital since the end of major combat in the U.S.-led war to oust Saddam Hussein six months ago.
"These terrorists are targeting the very success and freedom we are providing to the Iraqi people," Mr. Bush said in a Rose Garden press conference. "Desperate attacks on innocent civilians will not intimidate us."
"I would assume they're either, or probably both, Baathists and foreign terrorists," the president said.
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.
A car bomb exploded Tuesday in the tense city of Fallujah and killed at least four people, a day after dozens died in a string of bombings in Baghdad.
Later Tuesday, eight massive explosions were heard in Fallujah, coming from the southern area of the city. U.S. officials in Baghdad said they were unaware of the explosions, which residents described as "deafening."
Elsewhere, four American soldiers were wounded near the northern city of Mosul, and a blast was reported in the southern city of Basra.
In other developments:
The attacks Monday occurred at the start of the Muslim fasting month of Ramadan and left scenes of broken bodies, twisted wreckage and Iraqis unnerved by an escalating underground war. The dead included eight Iraqi policemen, at least 26 Iraqi civilians and a U.S. soldier.
Coming a day after a rocket barrage Sunday on a hotel where Deputy Defense Secretary Paul Wolfowitz was staying, the bombings attested to the spike in resistance by opponents of the American occupation.
The attacks also shook the confidence of international organizations that were taking part in the reconstruction of Iraq.
Secretary of State Colin Powell urged the Red Cross and other nongovernment organizations — as well as foreign contractors and the United Nations — to stay in Iraq.
"They are needed. Their work is needed. And if they are driven out, then the terrorists win," Powell said Monday in Washington.
Antonella Notari, chief spokeswoman at ICRC headquarters in Geneva, said no decision had been taken whether to evacuate non-Iraqi staff from Iraq. Twelve of the dead in Monday's attacks were killed in a car-bombing outside the Red Cross office in a quiet street in central Baghdad.
However, the German TV network ARD quoted the head of the ICRC delegation in Iraq as saying the evacuation of Red Cross personnel would begin Tuesday.
It is uncertain what groups carried out the attacks. In Baghdad, U.S. and Iraqi officials blamed foreign fighters intent on targeting those who cooperate with the American-led occupation. In Washington, however, Pentagon officials said they believed Saddam loyalists were responsible.
"The Baathists try to create chaos and fear because they realize that a free Iraq will deny them the excessive privileges they enjoyed," Mr. Bush said Tuesday. The foreign terrorists, he said, "fear a free and peaceful state in the midst of a world where terror has found recruits."
A coalition spokesman, Charles Heatly, said it was difficult to speculate on who was behind the attacks. He told the British Broadcasting Corp, that "there certainly are indications that there are foreign terrorists who are coming into Iraq," but he did not explicitly accuse them of responsibility.
Since Mr. Bush declared an end to major combat in Iraq on May 1, 113 U.S. soldiers have been killed by hostile fire, and about 1,675 have been wounded. U.S. forces come under attack an average of 26 times a day, and incidents have been on the rise since early September.