In an interview with Fox News Channel's Hannity and Colmes, taped in Florida on Saturday, the president was asked whether the country would always be vulnerable to another terror attack and whether Americans would always have to live with that.
"Yes, because we have to be right 100 per cent of the time in disrupting any plot and they have to be right once," Bush said. He said the country is safer from terrorism, but "whether or not we can be ever fully safe is up - you know, up in the air."
Excerpts from the interview were released Sunday.
Bush said he was sure terrorists still "think about" trying to disrupt the Nov. 2 election, citing the March 11 train bombings in Madrid that killed 191 people right before Spain's national elections.
"I don't want to alarm anybody because . . . there's nothing specific at this point in time - a kind of general intent," Bush said.
Bush caused a flap at the Republican convention in New York in late August when he said of the war on terror: "I don't think you can win it." The comment, made in an interview with NBC, complicated party efforts to portray him as a resolute leader.
The president quickly backed away from the earlier remark, asserting that the war on terror could be won, even if not in a conventional sense, and that he "probably needed to be more articulate."
In the Fox interview, Bush also was asked whether a nuclear, chemical or biological attack in the United States is a real possibility. "Yes it is," Bush replied. "That's the biggest threat we face."