President Bush and Sen. John F. Kerry returned to the campaign trail today after their first presidential debate, holding rallies in key battleground states as their campaigns sought to put the best face on their performance and sharpen their differences on national security issues.

With three television news polls showing that Kerry won last night's debate in Florida, Bush went on the offensive at a campaign rally in Allentown, Pa., hammering Kerry as inconsistent.

"Last night Senator Kerry only continued his pattern of confusing contradictions," Bush told supporters at the rally in one of the election's vital swing states. He charged, "My opponent has a fundamental misunderstanding of the nature of the war on terror, and he has no plan to win in Iraq." Bush accused Kerry of being "disdainful or dismissive" of countries that have contributed limited numbers of troops to a U.S.-led coalition in Iraq, and he said this was not the way to lead the coalition.

Bush seized on one of Kerry's answers to a question during the debate to claim that the Massachusetts senator wants to make U.S. national security decisions subject to foreign approval. In the process, Bush aimed a slap at France, which, along with Germany and several other allies, opposed Bush's decision last year to invade Iraq.

"Senator Kerry last night said that America has to pass some sort of global test before we can use American troops to defend ourselves," Bush asserted. "He wants our national security decisions subject to the approval of a foreign government. Listen, I will continue to work with our allies and the international community, but I will never submit American national security to an international test. The use of troops to defend America must never be subject to a veto by countries like France."

Democrats accused Bush of distorting Kerry's remarks, continuing what they describe as the Bush campaign's pattern of twisting the senator's words and mischaracterizing his positions.

"Bush has no plan for ending the chaos in Iraq but continues to give a rose-colored description of the situation there while giving blatantly false descriptions of John Kerry," said Phil Singer, a spokesman for the Kerry campaign. "Millions of Americans heard what John Kerry said and know that George Bush is distorting it today out of frustration."

Asked last night by moderator Jim Lehrer for his position on the concept of preemptive war, Kerry said: "The president always has the right and always has had the right for preemptive strike. . . . No president, through all of American history, has ever ceded, and nor would I, the right to preempt in any way necessary to protect the United States of America. But if and when you do it, Jim, you've got to do in a way that passes the test, that passes the global test, where your countrymen, your people understand fully why you're doing what you're doing and you can prove to the world that you did it for legitimate reasons."

Kerry added, "So what is at test here is the credibility of the United States of America and how we lead the world."

After the debate, Kerry remained in Florida to hold campaign rallies today in Tampa and Orlando.

In an appearance in Tampa, Kerry accused Bush of failing to take sufficient steps to improve U.S. national security.

"This president has relieved America of the homeland security that it deserves, and we're going to change that on November 2nd," Kerry declared.

He also pointedly took issue with Bush's comments about Kerry's position on Iraq. "He keeps trying to say, 'Well we don't want somebody who wants to leave, we don't want to wilt or waver,' " Kerry said. "Well, Mr. President, nobody's talking about leaving, nobody's talking about wilting and wavering, we're talking about winning and getting the job done right. Let's have the real debate."

Bush, after campaigning in Pennsylvania, planned to head to New Hampshire, another battleground state.

The two presidential candidates meet in St. Louis, Mo., next Friday for the second of three scheduled debates.

Vice President Cheney and Kerry's running mate, Sen. John Edwards of North Carolina, will debate each other Tuesday in Cleveland.

Edwards gave his own assessment of the Bush-Kerry debate at an appearance today before a large gathering in Huber Heights, Ohio, Washington Post staff writer Matthew Mosk reported.

"I think what America saw last night in John Kerry was a man of strength, vision, conviction -- a man who is ready to be the next commander in chief," Edwards told the crowd, which included about 150 undecided voters.

Citing one example of what he said was the president's penchant for making the same points "over and over and over," Edwards rejected Bush's criticism of Kerry for sending "mixed messages."

"Well, I don't know about you, but I heard a very clear message from John Kerry," Edwards said. "His message to the troops was, 'We are with you.' His message to the terrorists was, 'We will destroy you.' His message to the American people was, 'We will keep you safe.'"

Huber Heights is a suburb of Dayton in Montgomery County, which narrowly supported Democratic presidential candidate Al Gore over Bush in the 2000 election.

Earlier, Edwards took to the airwaves to play up Kerry's debate performance and knock Bush, whom he accused of refusing to acknowledge obvious problems in Iraq.

"You can't fix a problem if you're not willing to admit that mistakes have been made and that you have a problem," he told ABC's "Good Morning America."

White House Communications Director Dan Bartlett presented the Bush campaign's side on the morning news shows, saying the president was pleased with his performance last night and showed his leadership in the war on terrorism.

"We have very difficult work going on in Iraq," Bartlett said on NBC's "Today" show. "And what President Bush has demonstrated is that we have a strategy and the resolve to see this through."

Interviewed on the Fox News Channel, Bartlett denied that Bush had been tired and emotionally drained from visiting hurricane victims in Florida earlier in the day, calling that notion "ridiculous."

Post-debate polls gave the edge to Kerry in the candidates' first meeting, although it was not clear whether winning the debate would translate into any appreciable gain in support heading into the Nov. 2 election.

A CBS News poll of uncommitted voters who watched the debate on television showed that 43 percent thought Kerry had won the debate, 28 percent picked Bush as the winner, and 29 percent considered it a tie.

According to the poll, 53 percent of the debate-watchers had a better opinion of Kerry after the event, while 22 percent had an improved opinion of Bush. On the key question of whether the candidates have a clear plan for dealing with the situation in Iraq, 52 percent said after the debate that Kerry has such a plan, compared to 14 percent who felt that way before the debate. As for Bush, 39 percent of those polled after the debate said he has a clear plan, while 60 percent said he does not.

An ABC News poll of registered voters who watched the debate said 45 percent thought Kerry won, 36 percent believed Bush did, and 17 percent thought it was a tie.

A CNN/USA Today/Gallup poll also gave the edge to Kerry, who was picked as the winner over Bush by 53 percent to 37 percent among registered voters who watched the debate. Although the Bush campaign has promoted the president as a leader who clearly speaks his mind, 60 percent of those polled in the CNN survey said Kerry had expressed himself more clearly than Bush during the debate.