President Bush and John F. Kerry head toward their final debate on Wednesday night pursuing divergent strategies, with Bush seeking to discredit his rival on terrorism and taxes while rallying his conservative base, and with Kerry aiming at swing voters with stepped-up attention to domestic issues.

Energized by Friday's presidential debate, Bush and Kerry hit the campaign trail early yesterday. The president renewed his attacks on Kerry as he campaigned in Missouri, Iowa and Minnesota, saying the challenger's assertions that he has held a consistent position on Iraq "just don't pass the credibility test." Kerry, in Ohio, accused Bush of making a series of "wrong choices" as president, and he tried to tap into discontent about Bush's policies by promising a new direction for the country.

Bush boosted Republican morale with his performance at the town-hall-style debate, but several instant polls judged Kerry a narrow winner. More than changing the dynamic of a race that has tightened in the past 10 days, Friday's debate served to set up Wednesday's encounter in Arizona as an opportunity to provide momentum to one of the candidates going into the final weeks of the election.

The central tension of the campaign was on clear display at the St. Louis debate, with Kerry determined to keep voters focused on what he called the failures of Bush's Iraq and economic policies and with Bush trying to force a close look at Kerry's past positions on Iraq and a 20-year record in the Senate that the president has characterized as mediocre.

Before the debates began, Bush held the edge both in national polls and in potential electoral votes. Since then, national polls have tightened and the electoral map has grown more competitive. Strategists on both sides believe it is likely that whoever wins at least two of the three biggest prizes -- Ohio, Florida and Pennsylvania -- will win the election.

With Bush pinned down by troublesome news about his Iraq policies, Kerry has tried to use the debates to boost his acceptability as a potential commander in chief and win the election with a strong focus on issues such as health care, the economy and stem cell research, where his advisers believe his positions are more popular than Bush's.

But the president's advisers took hope from what they believe was a solid performance by Bush in the domestic portion of Friday's debate -- a view shared privately by some Democratic strategists. As the next official debate turns to domestic issues, the president is stepping up attacks on Kerry as a liberal who will raise taxes and turn health care over to the federal government.

Bush plans to question Kerry's promise in Friday's debate never to raise taxes for Americans making less than $200,000 by citing the Democrat's past votes for tax increases, an aide said. Privately, Republicans say this was one of Kerry's more effective lines in the debate and one that could soothe voter concerns about Democrats raising taxes over the next four years. The president will continue to talk more about what he says are flaws in Kerry's plans rather than focusing on Bush's agenda on health care and taxes.

Still, the Bush campaign remains convinced that terrorism and national security will decide this election. At a morning fundraiser for Republican gubernatorial candidate Matt Blunt in Missouri, Bush ridiculed Kerry's position on Iraq, saying he has been too inconsistent to trust. "With a straight face, he said, 'I only had one position on Iraq,' " Bush said. "He must think we've been on another planet."

Campaigning in Florida on Saturday, Vice President Cheney noted that at one point Kerry had said Hussein was a threat but that later he chastised Bush for being "preoccupied with Iraq, where there wasn't a threat." Cheney said, "That's unbelievable, . . . mind-boggling."

After Bush's disappointing performance at the first debate in Coral Gables, Fla., Bush advisers signaled a belief that their candidate had rebounded. But Kerry advisers see openings to raise doubts about where Bush would take the country, particularly on domestic policy. They want to make the election a referendum on change.

Democratic pollster Stanley Greenberg said Kerry made clear gains, particularly with independent and undecided voters, Friday night, according to his research. "After the debate, fewer people thought that John Kerry was a flip-flopper or too ready to raise taxes," he said.

Wednesday's debate at Arizona State University will focus exclusively on domestic issues. Although Kerry appeared defensive at points during that part of Friday's debate that covered domestic issues -- particularly on abortion -- Kerry advisers said their own research during the debate showed positive reactions from a selected group of voters on health care, prescription drugs, jobs and stem cell research.

On both abortion and stem cells, the competing Bush and Kerry strategies were clear, with Bush playing directly to social and religious conservatives and Kerry reaching out to swing voters and women.

The Kerry campaign already has a television commercial airing in some battleground states featuring actor Michael J. Fox, who has Parkinson's disease, that calls for expanded research using embryonic stem cells. Greenberg told reporters yesterday that Kerry had scored particularly well with college-educated voters on that question.

Kerry advisers said they believe the senator's performances in the debates are helping to erase questions about his fitness to serve as commander in chief, a vital threshold for the challenger to cross. They also said that whenever external events warrant, they will hammer Bush on his Iraq policies, as they did this past week after a new report showed that Iraqi President Saddam Hussein had neither weapons of mass destruction nor the capacity to produce them at the time of the war.

But senior Kerry adviser Joe Lockhart told reporters the campaign hopes to spend the final weeks talking mostly about domestic issues. "We're very much looking forward to Wednesday night, where it's 90 minutes of domestic issues and will really allow us to frame up what we will think will be the last . . . three weeks of the campaign," he said.

Despite some small differences, Kerry and Bush strategists largely agree with each other on how the electoral map shapes up. Bush's once-strong lead in Ohio has eroded, according to various polls and private assessments. Florida remains tight, and the hurricane-racked state has been a pollster's nightmare for the past month. Neither campaign takes either state for granted at this point. Pennsylvania has begun to move toward Kerry, but Bush will fight for it until the end.

The upper Midwest remains the principal battleground. Kerry has the edge in Michigan, but Bush has been leading in Wisconsin. Kerry advisers say the state has begun to move back in their direction but will be hard-fought until the election. Iowa remains even more problematic for Kerry at this point.

Minnesota continues to lean toward Kerry, but Bush campaigned there yesterday. Missouri appears to be Bush country right now. Kerry has stopped advertising there, and his advisers show no signs of trying to compete seriously there unless the overall race moves more dramatically.

The year began with four western states as potential battlegrounds: New Mexico, Arizona, Nevada and Colorado. Arizona looks good for Bush, according to both campaigns. New Mexico, which Al Gore won by fewer than 400 votes in 2000, remains highly competitive, as does Nevada, a Bush state four years ago. Kerry advisers say they will continue to fight for Colorado, and Bush advisers express some concern about the state.

Bush plans to campaign in the Northwest after the Arizona debate, with stops in Oregon, where Kerry has a narrow lead. But Republicans fear Kerry may be in solid shape in Washington.

Several smaller states continue to occupy the campaigns. New Hampshire, a Bush state four years ago, is a battleground Kerry aides believe they can win. In Maine, one of two states without a winner-take-all policy for the electoral college, Kerry's advisers predict he will win the overall vote but worry that Bush could steal one electoral vote by winning the state's northern congressional district. A senior Bush campaign official said West Virginia, which voted for the president in 2000, is moving strongly in Bush's direction, and Democrats agree that Kerry's positions on cultural and social issues are tough to overcome there.

Republicans still hold out hope of a major upset in New Jersey, a Democratic state where polls have shown as closer than expected. In a sign of concern inside the Kerry camp, Edwards has visited the state twice in nine days. Cheney will speak there Monday. But a top Kerry aide said the campaign doubts a candidate such as Bush, who opposes abortion and gun control, can win there.

Bush campaign manager Ken Mehlman said he believes that only 6 to 8 percent of voters remain undecided. "They don't vote, or they split between the two candidates," he said. But Kerry officials still see undecided voters more likely to side with the challenger. Bush officials say the dynamics of the race are set in stone and only an outside event such as a terrorist attack or major development in Iraq will shake it up. "We are in a different world, because there are a small number of undecided voters and a large volume of information for all voters," Mehlman said. "This is not a situation where there are a large number of voters who are getting their first look."

At a fundraiser in Jacksonville, Fla., Vice President Cheney takes a swipe at comments John F. Kerry made during Friday night's debate.Sen. John Edwards, the Democratic vice presidential nominee, addresses a rally at Detroit Urban Lutheran High School. Kerry has an edge in Michigan.