The opportunity for terrorists to try to influence the election, as was the case last month in Spain, appears to be an opportunity that would "be too good to pass up for them," Rice said.
"I think that we do have to take very seriously the thought that the terrorists might have learned, we hope, the wrong lesson from Spain," Rice said on a Sunday morning talk show.
"I think we also have to take seriously that they might try during the cycle leading up to the election to do something," she said.
"We are actively looking at that possibility, actively trying to see — to make certain that we are responding appropriately," she said.
Jose Maria Aznar, outgoing prime minister of Spain and a strong U.S. ally in the war in Iraq, says he has warned President Bush that he believes terrorists will try to affect the U.S. election as they did in Spain.
On March 11, terrorists blew up a rail line in Madrid, killing 191 and injuring 1,800 others.
"I told George Bush, and (British Prime Minister) Tony Blair and other political leaders to be extremely careful before elections ... and to be very vigilant," Aznar said in a broadcast interview.
Aznar's Popular Party was favored to win the election until the four commuter trains were attacked. "It is obvious that these attacks were looking for a political effect," he said.
Socialist leader Jose Luis Rodriguez Zapatero, who succeeded Aznar over the weekend, was holding his first cabinet meeting on Monday.
Spanish newspapers El Pais and ABC reported that his foreign minister, Miguel Angel Moratinos, will travel to Washington this week to meet with Secretary of State Colin Powell and Rice.
El Pais reported that Moratinos will offer non-military cooperation in Iraq, such as training of Iraqi police, as an alternative to the Spanish soldiers' presence if Zapatero does decide to bring them home. The Foreign Ministry declined comment Sunday.
Zapatero plans to pull Spanish troops from Iraq by June 30 unless the United Nations takes over political and military control of the occupation.
"That will not be good for Spain, not a good day for the coalition, and a very good day for those who don't want stability and democracy in Iraq," Aznar said.