WASHINGTON – On the first day of a Republican National Convention aimed at portraying him as a resolute anti-terror leader who is not prepared to yield to America’s foes, President Bush prompted a storm of Democratic criticism by suggesting in a television interview aired yesterday that the war against terrorism may not be totally winnable.

Interviewed on NBC’s “Today” show, Mr. Bush was asked, “Do you really think we can win this war on terror in the next four years?”

Mr. Bush replied, “I have never said we can win it in four years.”

NBC’s Matt Lauer rephrased the question: “So I’m just saying can we win it? Do you see that?”

Mr. Bush said: “I don’t think you can win it. But I think you can create conditions so that those who use terror as a tool are less acceptable in parts of the world.”

Pressed further by Mr. Lauer about whether Mr. Bush’s future grandchildren would be reading about Al Qaeda in the newspaper every day, Mr. Bush replied, “I can’t tell you. I don’t have any … definite end.”

Fearing that the remark could overshadow the first day of the GOP convention, or at least undermine the strong leadership message they were seeking to portray, White House aides sought to take back the president’s remarks. A White House aide told The New York Sun that the president “in a sense misspoke, in a sense it was a gaffe.” He added: “What he meant was that the war will be a long war and that Al Qaeda is never going to raise the white flag.”

Nonetheless Democrats seized on the president’s remark. Senator Kerry’s running mate, Senator Edwards, led the way by saying “this is no time to declare defeat,” although Mr. Edwards acknowledged also that defeating terrorism “won’t be easy and it won’t be quick.”

Mr. Edwards said: “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.”

In a news conference organized by the Democrats, retired General Merrill McPeak, a former Air Force chief of staff, also responded to Mr. Bush’s remark, saying, “I decided a year ago that he cannot win the war on terror.”

White House spokesman Scott Mc-Clellan insisted that the Democrats were missing the point of what Mr. Bush had in mind. “I don’t think you can expect that there will ever be a formal surrender or a treaty signed like we have in wars past,” he said. “That’s what he was talking about. It requires a generational commitment to win this war on terrorism.”

In his interview with NBC, Mr. Bush said it was essential for America to stay the course and make the world safer for future generations. Mr. Bush argued that retreating from the war on terror “would be a disaster for your children.”

“You cannot show weakness in this world today because the enemy will exploit that weakness,” he said. “It will embolden them and make the world a more dangerous place.”

Campaigning today in Nashua, N.H., Mr. Bush foreshadowed his convention speech. “Let me tell you an interesting story. It’s so good, I may use it next Thursday night,” he said, joking, “Ignore I said that.”

He said that in the Oval Office, “The door opens up, and in walks seven guys who have got Xs carved in their foreheads and their right hands had been cut off by Saddam Hussein’s henchmen. And they came in to see me. They – they had been in Houston, Texas, where they had new hands put on because of the generosity and the compassion of people who live in the free world.”

“It was overwhelming for me. I’m kind of a crier sometimes. And the contrast was so unbelievably powerful, the difference between a society where a tyrant can whimsically cut off a poor guy’s hand, and a society that is compassionate enough to help heal that hurt. This guy takes his pen and he writes a prayer to America,” Mr. Bush said.

Also in Nashua, Mr. Bush was asked a question hostile to Israel’s prime minister. “How can Ariel Sharon, as you’ve said, be a man of peace if he causes death and torture among innocent Palestinians every day? How can Ariel Sharon be a man of peace if he fits your definition a terrorist?” the questioner asked.

Mr. Bush responded, “Ariel Sharon is defending his country against terrorist attacks, just like we will …Ariel Sharon is a duly-elected official in a democracy. In other words, Israel is a democracy. We would hope that the Palestinians would have that same kind of democracy which would lead to a more peaceful world.”

Earlier in his Nashua remarks, Mr. Bush had made reference to the war in Iraq and to Saddam Hussein’s support for terrorism. “Remember Abu Nidal? Leon Klinghoffer? He was the guy that was murdered because he happened to be Jewish. The Abu Nidal organization was housed and based out of Baghdad. That is a terrorist organization,” Mr. Bush said.