On the campaign trail in New Hampshire, Mr. Bush sought to emphasize the economy, but his comments on terrorism dominated national attention.
In an interview on NBC-TV's "Today" show, Mr. Bush vowed to stay the course in the war on terror, saying perseverance in the battle would make the world safer for future generations. But he suggested an all-out victory against terrorism might not be possible.
Asked "Can we win?" Mr. Mr. Bush said, "I don't think you can win it. But I think you can create conditions so that the — those who use terror as a tool are less acceptable in parts of the world."
Democrats, looking for ways to deflect the spotlight from Republicans as they opened their convention in New York, pounced.
"After months of listening to the Republicans base their campaign on their singular ability to win the war on terror, the president now says we can't win the war on terrorism," said Democratic vice presidential candidate John Edwards. "This is no time to declare defeat."
"I decided a year ago that he cannot win the war on terror," said retired Gen. Merrill McPeak, former Air Force chief of staff, at a news conference in New York organized by Democrats.
White House spokesman Scott McClellan sought to clarify the president's remarks, telling reporters, "He was talking about winning it in the conventional sense ... about how this is a different kind of war and we face an unconventional enemy."
"To suggest that the war on terror can't be won is absolutely unacceptable," said Sen. Joseph Biden, D-Del., the senior Democrat on the Senate Foreign Relations Committee.
"First George W. Bush said he miscalculated the war in Iraq, then he called it a catastrophic success and blamed the military," said Kerry spokeswoman Allison Dobson. "Now he says we can't win the war on terror. Is that what Karl Rove means when he calls for steady leadership?"
Meanwhile Rove, Mr. Bush's chief political strategist, acknowledged that the continuing conflict in Iraq could be a political liability in key swing states such as Pennsylvania, Florida and Arizona.
"We're in a war, so you got a lot of people who say, 'I don't like the fact that we're in a war. But I want to win the war,'" Rove said in an interview in New York with Pennsylvania reporters.
The coordinated Democratic attack came as Republicans sought to portray Mr. Bush as a strong leader in the war on terrorism in the opening session of the Republican National Convention.
Mr. Bush suggested in an interview with Time magazine that he still would have gone into Iraq but with different tactics if he had known "that an enemy that should have surrendered or been done in escaped and lived to fight another day."
He called the swift military offensive that led to the fall of Baghdad in April 2003 "a catastrophic success" in light of the fact that fighting continues to this day despite the overthrow of Saddam Hussein's government.