"Terrorists want to break our will and resolve," White House spokesman Scott McClellan said. "They want us to cut and run.
"Terrorists must not be allowed to think they influence elections or that they influence policy. That would be a terrible message to send."
Jose Luis Rodriguez Zapatero, an ardent opponent of the war in Iraq and continuing U.S.-led occupation, took control of Spain's prime ministership Sunday when his Socialist Party unexpectedly beat out the hand-picked Popular Party successor to Jose Marie Aznar, a strong supporter of Bush in the war.
Zapatero has vowed to bring back from Iraq Spain's 1,300 soldiers.
Bombings in Madrid Thursday killed 200 people and injured more than 1,400 others.