Vice President Cheney and the campaign of Sen. John F. Kerry traded gibes today over the fight against terrorism, with Cheney ridiculing Kerry's recent vow to wage a "more sensitive" war and the Democrat's campaign accusing the vice president of distortion and hypocrisy.

Cheney, addressing a campaign rally in Dayton, Ohio, delivered a lengthy denunciation of Kerry's national security posture while extolling the leadership of President Bush.

"Senator Kerry has also said that if he were in charge, he would fight a more sensitive war on terror," Cheney said to laughter from the audience, which included many veterans.

"America has been in too many wars for any of our wishes, but not a one of them was won by being sensitive," Cheney said. "President Lincoln and General Grant did not wage sensitive warfare, nor did President Roosevelt, nor Generals Eisenhower and MacArthur."

He said that "a sensitive war will not destroy the evil men who killed 3,000 Americans" in the Sept. 11, 2001, terrorist attacks and "who seek the chemical, nuclear and biological weapons to kill hundreds of thousands more." Nor would those who have beheaded Americans "be impressed by our sensitivity," Cheney said.

"As our opponents see it, the problem isn't the thugs and murderers that we face, but our attitude," he said. "Well, the American people know better. . . . Those who threaten us and kill innocents around the world do not need to be treated more sensitively. They need to be destroyed."

Cheney's comments culminated a series of increasingly aggressive attacks against the Massachusetts senator in recent days, perhaps the most critical levied by the vice president against Kerry, staff writer Mark Leibovich reported from Dayton. Cheney's speech today -- to an invitation-only crowd of 500 supporters comprised heavily of veterans -- was the last stop a two-day swing through the battleground states of Missouri, Michigan and Ohio.

Kerry's "more sensitive" war remark was also raised Wednesday at a Cheney campaign event in Joplin, Mo., where the vice president and his wife, Lynne, co-hosted a "Town Hall" meeting for another group of invited guests. "Senator Kerry has made the statement that he would fight a more sensitive war on terror," one local supporter asked Lynne Cheney. "What in the world would he be thinking about there?"

To which Lynne Cheney replied, "I just kind of shook my head when I heard that. With all due respect to the senator, it all sounded so foolish."

In response to Cheney's speech today, a spokesman for the Democratic presidential nominee dismissed Cheney's remarks as "another disingenuous attack" that distorts what Kerry said and contradicts comments by Bush. At issue was a passage in a speech that Kerry, a four-term senator from Massachusetts, delivered to a conference of minority journalists in Washington, D.C., last week.

"I will fight this war on terror with the lessons I learned in war," Kerry said. "I defended this country as a young man, and I will defend it as president of the United States. I believe I can fight a more effective, more thoughtful, more strategic, more proactive, more sensitive war on terror that reaches out to other nations and brings them to our side and lives up to American values in history."

Kerry spoke of his strategy "to strengthen our military, to build and lead strong alliances and reform our intelligence system." He said he would "win the peace in Iraq" and "get the terrorists wherever they may be before they get us."

Cheney does not understand "that arrogance isn't a virtue, especially when our country is in danger," Kerry campaign spokesman Phil Singer said in a statement. "Alienating allies makes it harder to hunt terrorists and bring them justice. If Dick Cheney learned this lesson instead of spending his time distorting John Kerry's words, this country would be a safer place."

The statement also pointed out that Bush had spoken of the need for American sensitivity at the same conference, called "Unity: Journalists of Color," the day after Kerry's address.

In response to a question on how to balance the pursuit of terrorists with preserving the civil liberties of Arab Americans and Muslims, Bush said, "Now, in terms of the balance between running down intelligence and bringing people to justice obviously is -- we need to be very sensitive on that."

In 2001, the Kerry campaign statement noted, Bush had said, "Precisely because America is powerful, we must be sensitive about expressing our power and influence. Our goal is to patiently build the momentum of freedom, not create resentment for America itself." Bush pledged that in dealings with other nations, "we will display the modesty of true confidence and strength."

Campaigning in California today, Kerry promoted his plan to build a stronger economy and create new jobs as he neared the end of a two-week, cross-country tour following his nomination at the Democratic National Convention in Boston at the end of July.

Bush also scheduled a campaign appearance today in California -- a fund-raising dinner in Santa Monica -- following a stop in Las Vegas, where he was addressing a carpenters' union gathering.

Tonight, Bush and his wife, Laura Bush, are scheduled to be interviewed jointly on CNN's "Larry King Live" at 9 p.m. EDT.