WASHINGTON – Is the Bush administration’s decision to de-emphasize use of the phrase “war on terror” an unheralded concession to last year’s unsuccessful Democratic presidential nominee, Senator Kerry of Massachusetts?

The White House says no, but some of Mr. Kerry’s backers contend the recent move to recalibrate the rhetoric of top administration officials away from the “global war on terror” and toward a “global struggle against violent extremism” amounts to a quiet vindication of the four-term Democratic senator.

“I think John Kerry had it right and the president had it wrong,” a former senator of Nebraska, Robert Kerrey, said in an interview. “It’s largely a recognition of what most people who have followed this have concluded long ago, which is that terrorism is a tactic that is used by certain extreme groups,” Mr. Kerrey, who is president of the New School University, said.

“Words matter,” a former ambassador to the United Nations and top foreign policy adviser to Mr. Kerry, Richard Holbrooke, said. “They were just playing campaign hardball. They were wrong on this. They fixed it.”

During the hard-fought presidential race, President Bush and Vice President Cheney hammered Mr. Kerry for allegedly being reluctant to use the phrase “war on terror” to describe the conflict facing America in the wake of the September 11, 2001, attacks.

“Some are skeptical that the war on terror is really a war at all. Just the other day, my opponent indicated that he’s not comfortable using the word ‘war’ to describe the struggle we’re in. He said, ‘I don’t want to use that terminology,'” Mr. Bush told donors at a fund-raising reception in Houston on March 8, 2004. “He also said the war on terror is far less of a military operation and far more of an intelligence-gathering, law enforcement operation. I strongly disagree.”

At a fund-raiser in South Dakota the following day, Mr. Cheney launched a similar salvo at the Democratic nominee. “Senator Kerry said he wasn’t even comfortable calling this a war. He said, ‘I don’t want to use that terminology,'” Mr. Cheney said.

The line of criticism emerged from the president and vice president again in October, after Mr. Kerry was quoted in a New York Times Magazine interview comparing the scourge of terrorism to intractable problems like prostitution or illegal gambling that could someday be reduced to a mere “nuisance.”

A White House spokesman, Trent Duffy, said Mr. Bush continues to stand by his criticism of Mr. Kerry’s stance. “The president took issue and still takes issue with those who think that the war on terror is a law enforcement matter. That’s the issue the president took up in the campaign,” the spokesman said, stressing that the president has not dropped the “war on terror” language completely. “Whatever Senator Kerry was calling the war on terrorism, he wasn’t calling it an ideological struggle. I don’t see how it’s a vindication of what he said then or now,” Mr. Duffy said.

A spokesman for the National Security Council, Frederick Jones, said the administration’s decision to use less war rhetoric and make more mention of the dangers of extremism is a response to the changing threat.

“The president has always said this is a war of ideas, and as this fight against extremism has evolved, I think you’re seeing a recognition of that evolving nature,” Mr. Jones said. “You may see more of this language, this greater understanding of it as a war of ideas, a war against extremism, as opposed to just a war on terrorism, which conjures up the image of military engagement.”

In a brief interview with The New York Sun last week, Mr. Kerry said the timing of the move to less militaristic talk struck him as odd.” They said, ‘You can’t win the war on terror,'” the former Democratic nominee said, referring to Mr. Bush’s quickly retracted statement last August that complete victory over terrorism was not possible. “Now, they’re saying, ‘There is no war on terror.’ And all the while there are additional bombings in London and Egypt, and Osama bin Laden is at large, and homeland security is underfunded,” Mr. Kerry said. “My concern is not with what to call it, they can wrestle with that, my concern is that they deal with the problem of extreme – terrorist extremism, whatever you want to call it, that they deal with it more effectively and tell the truth to the American people about it.”

Asked if the administration was coming around to his view, the senator said, “That’s for others to judge. I don’t want to spend my time on that.”

Despite the attacks he weathered during the campaign, Mr. Kerry never publicly disavowed the use of the term “war on terror.” In fact, he used that phrase repeatedly in his speeches. However, the senator did say in the March 2004 interview quoted by Messrs. Bush and Cheney that the ideological and economic aspects of the fight were ultimately more important than military action, and that it was best not to describe the nonmilitary engagement as a “war.”

And during the campaign, Mr. Kerry’s chief foreign policy adviser, Mr. Holbrooke, openly scoffed at the notion of a war on terror. “We’re not in a war on terror, in the literal sense,” he told the Times.

That analysis seems to be winning converts. Speaking in Washington last week, the chairman of the joint chiefs of staff, Richard Myers, said he has “objected to the use of the term ‘war on terrorism.'” He called the problem “more diplomatic, more economic, more political than it is military.”

The rhetorical change has been most noticeable in appearances by Defense Secretary Rumsfeld, who now regularly refers to a “global struggle against extremism.” The transition was first noted last week by the Times, which said the new focus was the result of high-level discussions that began in January.

A longtime advocate for a change in the “war on terror” rhetoric, Daniel Pipes, said he was pleased with the administration’s move. “‘Global struggle against extremism’ is only halfway there,” said Mr. Pipes, who is a columnist for the Sun and director of a Philadelphia-based think tank, the Middle East Forum. “The next step is what we’re evolving to know, which is a war on radical Islam,” he said. “I think the word Islam needs to be in there. Jihad is okay if you must.”

“This is such an improvement in clarity,” a former speechwriter for Mr. Bush, David Frum, said, even as he called the adjustment “slow progress.”

“Basically, the problem was the phrase ‘war on terror’ meant you were making war on a ‘what.’ This now shifts from making a war on a ‘what’ to making war on a ‘who,'” he said.

Still, Mr. Frum said he would be wary of adding a reference to Islam to the formulation. “There are a lot of powerful reasons for the U.S. government not to make use of the word ‘Islamic,'” the former speechwriter said.

Mr. Holbrooke said he also favors skipping the Islam reference. “I would use the phrase, ‘Al Qaeda and its allies,'” he said. “We know the name of the inspirational leader of our enemy. We know it very well, just as surely as we knew the name Adolf Hitler. Osama bin Laden, he exists, and has a theory as clearly defined as ‘Mein Kampf.’ Why don’t we attack him and his supporters daily, by name and continually? … I simply don’t know why they don’t just name the name of the evil villain of our time.”

Oddly, Mr. Bush himself is among those who have expressed skepticism about the ‘war on terror’ formulation. Last August, well before the presidential campaign entered the final stretch, Mr. Bush said the slogan was a mistake.

“We actually misnamed the war on terror. It ought to be the struggle against ideological extremists who do not believe in free societies who happen to use terror as a weapon to try to shake the conscience of the free world,” Mr. Bush told a convention of minority journalists. The unwieldy description prompted laughter from the moderator of the discussion, but the president made it clear he was not joking.