WASHINGTON – President Bush and Senator Kerry scrapped furiously yesterday for votes in the critical states of Florida and Ohio, searching for last-minute support as the bruising election race entered its final 48 hours without any clear guide from national or battleground opinion polls as to who will win tomorrow.

The president campaigned from one end of Florida to the other before flying to Ohio for a rally in Cincinnati, as Mr. Kerry sped north from Ohio to New Hampshire before arriving in Tampa, Fla. Their running mates and their prominent supporters, such as Senator Clinton, also stumped energetically in New Jersey, Hawaii, Arkansas, and the key Midwest states of Iowa, Minnesota, Pennsylvania, and Michigan.

Republicans pointed to a Newsweek poll giving the president a four-percentage-point lead over his Democratic rival as evidence the race is breaking their way, but tracking polls from the Washington Post and Fox News suggested that the contest is deadlocked when it comes to the national vote and will be determined finally by which campaign mounts the best get-out-the-vote effort on Election Day.

Pollsters are raising the prospect of a repeat of 2000, with a candidate losing the popular vote but winning the presidency. With the race so tight, both campaigns were expected to mount the biggest-ever national efforts to get their base vote out on Election Day.

Both campaigns sought yesterday to turn to their advantage the reemergence of Al Qaeda leader Osama bin Laden, pointing to the terrorist mastermind’s menacing 14-minute videotape to the American people Friday as proof that their candidate is on the right track when it comes to the war on terror.

Without referring to the tape directly, Mr. Bush emphasized his commander-in-chief credentials, saying, “If you believe America should fight the war on terror with all her might and lead with unwavering confidence, I ask you, come stand by me.”

Senator McCain of Arizona argued on the morning talk shows that voters are more likely to perceive the tape as an affirmation of Mr. Bush’s stance that the terrorist threat is very much alive and needs to be combated forcefully. The Republican said the tape will assist the president more than it will aid Mr. Kerry because it “focuses undecided voters on the transcendental issue of the election, “the war on terror, and that “plays to the president’s advantage.”

In an interview with ABC to be aired in full tonight, Mr. Kerry rejected suggestions that Mr. bin Laden’s intervention would assist his opponent.

“America knows that I bring 35 years of experience, more experience than George Bush has in foreign affairs and national-security affairs,” the Democrat said. “I’m going to hunt down, capture, and kill the terrorists.”

The president has consistently polled better than the senator on the issue of fighting terrorism, and Kerry campaign aides privately appeared anxious yesterday about the possible electoral fallout from the bin Laden tape. Publicly, though, they insisted the video message would prompt in voters’ minds questions about why Mr. Bush had failed to capture or kill the man behind the September 11 terror attacks.

Kerry adviser Robert Shrum accused Mr. Bush of diverting resources from the hunt for bin Laden by launching the invasion of Iraq. “The issue is that we diverted our forces and our focus from Afghanistan. We went to Iraq. We created a mess in Iraq. It’s a terrorist haven that it wasn’t before,” he told “Fox News Sunday.”

That earned a rebuke from Bush adviser Karen Hughes, who accused the Democratic camp of politicizing Mr. bin Laden’s 11th-hour appearance. She said it was “just shameful” that Mr. Kerry “would try to use that to score political points,” saying that instead it was “a moment for all Republicans, all Democrats, and all Americans to express our revulsion at this face of evil.”

Later yesterday, Vice President Cheney said Senator Kerry’s first response to the bin Laden videotape was to take a poll to find out what he should say about it, the Associated Press reported.

A spokesman for Mr. Kerry’s campaign, Joe Lockhart, did not deny conducting a survey about the tape, but he suggested Mr. Bush had done so as well. Bush campaign strategist denied asking any poll questions about the Al Qaeda terrorist.

In keeping with Democratic misgivings about the bin Laden video and its possible effect on the election, Mr. Kerry did not dwell on the war on terror yesterday. He left it to surrogates to address the tape, while he focused instead on domestic pocketbook issues. The Democratic nominee criticized cuts in after-school programs and health-care coverage in the last four years, as well as the jobs lost. His aides believe that these are the issues that could sway undecided voters.

Both candidates courted religious and ethnic minority voters yesterday, with the president starting out his day in the battleground state of Florida, at tending a service at a Roman Catholic Church in Miami accompanied by the first lady and his brother, the Sunshine State’s governor, Jeb Bush. “Mr. President, I want you to know that I admire your faith and your courage to profess it,” said the officiating priest, Monsignor Jude O’Doherty.

Bush campaign advisers are hoping the president can pick up crucial support from non-Cuban Hispanics in Florida while maintaining the GOP lock on the Cuban vote. Speaking on CNN, the White House chief of staff, Andrew Card, predicted Mr. Bush would do better than expected among minority voters. A poll in the Miami Herald newspaper yesterday showed 61% of Hispanics supported Mr. Kerry and 33% backed the president.

Marking his fifth straight Sunday appearance at a church with a predominantly black congregation, Mr. Kerry quoted the Bible and criticized his White House rival at a Baptist service at Dayton, Ohio. “There is a standard by which we have to live,” the Democrat said. “Coming to church on Sundays and talking about faith and professing faith isn’t the whole deal.”

Later, in an interview with NBC’s Tom Brokaw, Mr. Kerry said he did not regret invoking Vice President Cheney’s daughter, Mary Cheney, who is gay, during a debate with President Bush.

“She’s made it a public thing. He’s made it a public thing. And all I was trying to do was honor the reality that people are who they are,” Mr. Kerry said.

The senator said Mr. Cheney’s prediction of a Bush/Cheney victory, 52% to 47%, was “bravado.”

“I hope America comes out and votes in record numbers, because this is the most important election of our lifetime,” Mr. Kerry said. “And I believe America can do better.”

In a separate interview with the AP, Mr. Kerry said if he lost tomorrow, he would not take the defeat personally but would be disappointed for the people he won’t be able to help. He added that if he wins, he would begin putting his Cabinet together “as fast as I can.”

Earlier yesterday, Mrs. Clinton campaigned at Newark’s Metropolitan Baptist Church. The visit by New York’s junior senator was the latest in a flurry by leading Democrats and Republicans to a state that Vice President Gore carried by 16 percentage points in 2000.

Polls in recent weeks suggest the president is gaining on Mr. Kerry, slicing a 13-percentage-point lead in one poll to four points in numbers released yesterday. A nationwide CBS poll last night had Mr. Bush up by three points with the president at 49% and Mr. Kerry at 46%.

Mrs. Clinton addressed New Jersey voters who are worried about “changing horses in midstream” during a crisis.

“If that horse you were on was headed right over the waterfall, you’d get off it, wouldn’t you?” she asked. “Some people say, ‘Oh, you know, the president is so consistent.’ Well, there’s no great virtue in being consistent for the sake of consistency, especially if you’re consistently wrong.”

New Jersey is one of a handful of states that are considered too close to call. A spate of new state polls show Messrs. Bush and Kerry tied in their top targets: Florida, Ohio, Pennsylvania, Wisconsin, Minnesota, New Hampshire, and New Mexico.