"Terrorists will kill innocent life in order to try to get the world to cower," President Bush told reporters. "They'll kill innocent people to try to shake our will. That's what they want to do. And they'll never shake the will of the United States."
Spain's newly elected Socialist prime minister has said he will pull 1,300 troops from southern Iraq unless the United Nations takes control of peacekeeping — a promise he made before the bombings.
"It is the wrong message to let terrorists think that they can influence policy, that they can influence elections," presidential press secretary Scott McClellan said.
Prime Minister Tony Blair, who stood with Mr. Bush and Aznar in favor of the Iraq invasion, said it was "hopelessly naive" to think that giving up in Iraq would lessen the threat from Islamic extremists.
"It is a war on our way of life, it is a war on our democracy, it is war on our freedom and that is why we must redouble our efforts and defeat it and the best way to do that is for the whole of the international community to stand firm on this," Blair told the House of Commons on Wednesday.
A day earlier, London's police chief and mayor warned that an attack might be inevitable.
"It would be miraculous if, with all the terrorist resources arranged against us, terrorists did not get through, and given that some are prepared to give their own lives, it would be inconceivable that someone does not get through to London," said Mayor Ken Livingstone.
French officials announced Tuesday they are investigating threats issued by a radical Islamic group against France and its overseas interests.
From Australia to Poland, countries with troops in Iraq fear they could be the next terrorist target, and the Bush administration acknowledged that U.S. allies could pay a price.
"Any country that allies itself with the United States, unfortunately, is a target," John Pistole, the FBI's executive assistant director for counterterrorism, told Sydney's 2UE radio station.
Australia's foreign minister promised that the government would not back away from the alliance.
"We will maintain our determination and our resolve to defeat terrorism, not to have our policies dictated by terrorists," Foreign Minister Alexander Downer told reporters.
In South Korea — which, like Spain, has deployed troops to Iraq — the acting leader called a meeting of senior officials to review anti-terrorism efforts, saying the country is a possible terrorist target.
"The main targets of terrorist attacks are countries sending troops to Iraq," Goh Kun was quoted as saying by his spokesman, Kim Duck-bong. "We are, in some respect, a country that should be on alert against terrorism."
Honduras said it will withdraw its 370 troops from the Spanish brigade in June — two months before they were to return home.
NATO allies on Tuesday agreed to widen their anti-terrorist naval patrols to the entire Mediterranean Sea as they began analyzing a Greek request for increased protection for this summer's Olympic Games.
The head of the Athens Organizing Committee insisted Tuesday that Greece was doing everything necessary to safeguard the Summer Olympics.
"The games will take place and whatever is needed for the games will be in place," Gianna Angelopoulos-Daskalaki said after meeting Premier Costas Caramanlis to review preparations in the wake of the deadly Madrid bombings.
The leaders of France and Germany said Tuesday that the deadly train bombings in Madrid underscore Europe's need for a joint plan to fight terrorism.
"All of Europe is the theater for terrorist actions," German Chancellor Gerhard Schroeder said. "So we must, together, as Europeans, confront this terrorism."
The investigation into Thursday's attack indicates a need for concerted action. So far, the probe is focusing on a web of suspected ties to indicted and convicted Islamic radicals.
Police in Britain are investigating whether a chief suspect in the Madrid bombings had links with British-based militants, the Guardian newspaper reports.
Renewed concern over terrorism spread beyond Europe. Interpol said more Asian countries have agreed to link up to a global police communications system and database designed to help capture terrorists and criminals prowling in disguise.
"The Madrid attacks are the reminder to the entire world, not just Europe, that these kinds of attacks can occur any day anywhere in the world, and we must try to prepare ourselves the best we can for them," Interpol Secretary General Ronald Noble said.
Even Colombia's largest rebel group, blamed for many of the nation's worst terrorist attacks, condemned last week's bombings as "outrageous."
Besides the security concerns they have sparked, the Madrid bombings could also have more political ramifications.
Italian Premier Silvio Berlusconi, for one, a close friend and ally of ousted Spanish Prime Minister Jose Maria Aznar, was seen at risk of isolation. Both Berlusconi and Aznar supported war in Iraq despite facing massive opposition by the citizens of their countries.
United Nations Secretary-General Kofi Annan said the Spanish government's initial insistence that Basque separatists were responsible for the bombings was a factor in Sunday's upset election victory by the Socialists.
But he said Tuesday that there were other factors as well, including strong public opposition to the U.S.-led war in Iraq.
In the United States, Democratic presidential candidate John Kerry expressed disappointment with incoming Prime Minister Jose Luis Rodriguez Zapatero's comments on the war.
"In my judgment the new prime minister should not have said he was going to pull out of Iraq," Kerry said. "He should have said this is going to increase our determination."
Former Democratic presidential candidate Howard Dean said that Mr. Bush's decision to send troops to Iraq appears to have contributed to the bombing deaths.
"That was what they said in the tape," Dean said. "They made that connection, I'm simply repeating it."