President Bush and Democratic challenger John F. Kerry returned to the campaign trail Friday and resumed the intense dispute over the Iraq war and homeland security that dominated the first presidential debate Thursday night.

After Kerry's strong performance in the showdown in Coral Gables, Fla., appeared to boost his candidacy, the two candidates pounced on remarks made during the lively foreign policy debate to open new lines of attacks and buttress old ones during campaign appearances in battleground states. Kerry said the administration has failed to sufficiently secure the United States from future attacks, while Bush accused his challenger of undermining U.S. troops fighting in Iraq.

As both campaigns struggled to determine how the widely watched debate had altered the race, Kerry told supporters at the University of South Florida that the president was resorting to Orwellian tactics to conceal the administration's failure to track terrorism suspects and prevent another strike on U.S. soil. Seizing on a new report that the government has not compiled a viable, unified terrorist watch list, Kerry said that "it's a complete failure, yet this president stands there and pretends to America that we're doing all that we can."

Bush, trying to fight back after what even some Republicans called a lackluster debate performance, said Kerry proved in their first face-to-face encounter that he lacks the clarity and consistency to triumph in Iraq, as well as the resolve to protect the United States without first getting the approval of other nations. "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 said in Allentown, Pa., before delivering a similar message in New Hampshire. "The use of troops to defend America must never be subject to a veto by countries like France."

It is too soon to determine whether Kerry has erased what both sides considered the president's narrow lead heading into the debate or changed the dynamics of a race that has trended Bush's way since the conventions. But Republicans and Democrats alike agreed that Kerry enhanced his chances of winning in November by hammering the president's credibility on Iraq and avoiding the meandering responses that have plagued him throughout the campaign. Some conservatives, such as Kate O'Beirne of the National Review, said Bush's performance was damaging. "I thought the president was repetitive and reactive," she said.

Sen. John McCain (R-Ariz.), who introduced Bush at his first post-debate rally, earlier called Kerry's performance the Democratic candidate's "brightest moment" of the past six weeks. But later at the rally, McCain said Bush proved "he has the strength, he has the courage."

Privately, some Bush aides reacted grimly to his showing and made few of the usual post-debate proclamations that their man had won the exchange. In an e-mail to reporters, the normally boastful Bush campaign suggested that the debate was a tie.

At the same time, Kerry appeared as confident as he did after the Democratic National Convention in July, hugging aides and advisers, who strained not to gloat. Kerry's family and friends celebrated his performance in the hotel bar, and several described the mood as similar to the one after Kerry's victory in the Iowa caucuses in January. If nothing else, Democrats -- including some Kerry aides who had grown increasingly concerned that the Massachusetts senator was on the verge of losing the race -- sounded reenergized -- and relieved.

Michael McCurry, a senior Kerry adviser, predicted that the polls, which show Bush with a single-digit lead, will not change noticeably in the immediate days ahead. But he said Kerry successfully set the stage for the next two debates, which will focus on domestic policy, by mitigating Bush's edge on which candidate is best prepared to win in Iraq and fight terrorism. "We believe people are taking a new, fresh look, and that's a very important achievement for us in the debate," he said.

Kerry's camp said Bush's biggest substantive blunder was suggesting that the country could not afford new homeland security measures. "I don't think we want to get to how he's going to pay for all these promises," Bush said. "It's like a huge tax gap."

Kerry shot back Friday: "My friends, this is the president who created a tax gap by providing a tax cut to the wealthiest Americans instead of investing in homeland security in the United States. Let's get real." Bush has dramatically increased spending on homeland security; Kerry says he would spend more, financed, in part by repealing the tax cuts for those making more than $200,000 a year.

McCurry said the president's biggest mistake in the debate was, perhaps, more stylistic. He compared Bush's gestures to those of the president's father, George H.W. Bush, who checked his watch and appeared uninterested during a 1992 debate with Bill Clinton. "It looked like there was nowhere else in the world that he did not want to be," McCurry said. News shows on Friday replayed images of the president scowling and appearing uneasy.

The Kerry campaign believes that images will bolster their strategy of portraying Bush as too stubborn and dismissive of those who do not share his political views. Conservatives voiced similar concerns in articles and Web postings. Scott McClellan, the White House press secretary, said Bush was simply showing how seriously he views terrorism and Iraq.

Kerry aides said they remain concerned about Bush's edge when voters are asked which candidate will keep the country safer. In his first stop on Friday, Kerry took on the charge Bush made nearly two dozen times during the debate: that the Democratic nominee is weak and wobbly. "He keeps trying to say, 'Well, we don't want somebody who wants to leave.' He says, 'We don't want to wilt and waver,' " Kerry said. "Well, Mr. President, nobody is talking about wilting and wavering. We're talking about winning and getting the job done right."

Kerry plans to shift strategies somewhat in preparation for the second debate next Friday in St. Louis, aides said. He will focus more on domestic issues such as the escalating costs of health care, education and energy, while continuing to pound the broader theme that Bush has made the wrong choice time after time, and that the American people are paying the price.

The president, meanwhile, traveled the length of the East Coast on Friday to continue to hammer away at Kerry's credibility in the face of danger, which Republicans see as his biggest liability. Bush immediately picked up where he left off in the debate, renewing his assault on Kerry for voting against an $87 billion spending measure for Iraq. "My opponent last night said our troops deserve better," Bush said. "They certainly deserve better than they got from Senator Kerry when he voted to send them to war and then voted against funding our troops in combat." Kerry voted to authorize the war in 2002 and against a spending bill two years later.

Recalling Kerry's statement that he voted both for and against the spending measure, Bush added: "Last night he said he made a mistake in how he talked about that vote. But the mistake wasn't what Senator Kerry said; the mistake was what Senator Kerry did. He voted against supplying our troops after voting for putting them in harm's way."

Ridiculing a previous Kerry statement that the vote was "protest," Bush said: "When we put American troops in harm's way, they certainly deserve better than to have a candidate for president use them as a protest."

The president and his aides sought to highlight an apparent contradiction in Kerry's arguments Thursday night. Bush noted that Kerry asserted that the war in Iraq is a mistake but then said that he did not believe U.S. troops in Iraq are "dying for a mistake," as the senator had said of the Vietnam War.

"You can't have it both ways," Bush said. "You can't say it's a mistake and not a mistake. You can't be for getting rid of Saddam Hussein when things look good and against it when times are hard. You can't claim terrorists are pouring across the border into Iraq, yet at the same time try to claim that Iraq is somehow a 'diversion' from the fight against terrorism.

But John Edwards, Kerry's running mate, predicted that voters will take away a much different message from the debate. "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 said at a campaign stop in Ohio.

Milbank is traveling with Bush. Staff writer Matthew Mosk, traveling with Edwards, contributed to this report.

The day after their first debate, John F. Kerry appeared at a rally in Tampa, while President Bush spoke in Manchester, N.H. The second debate is scheduled for next Friday in St. Louis.