BOSTON — President Bush was within a hair’s breadth of winning re-election this morning as the major battleground states of Florida and Ohio both appeared to have delivered their votes to the incumbent in the bitter presidential contest.

Those two states brought Mr. Bush’s tally in the electoral college to 274, more than the number needed to win the presidency. To defeat Mr. Bush, the Democratic nominee, Senator Kerry, needed to take back Ohio and win the outstanding battleground states of the Midwest.

Early this morning, Mr. Bush was leading in Iowa and New Mexico, making it unlikely that Mr. Kerry could carry off a sweep in all the states that were still in doubt. Mr. Bush was preparing to speak to supporters — and, aides quoted by the AP said — declare victory early this morning.

Early today, advisers to Mr. Kerry insisted that Ohio was still within the senator’s reach.

“It’s been a long night,” Senator Edwards said early this morning. “We’ve waited four years for this victory, we can wait one more night. Tonight, John and I are so proud of all of you who are here with us and all of you across the country who have stood with us in this campaign. John Kerry and I made a promise to the American people that with this election, every vote would count and every vote would be counted. Thank you. Tonight, we are keeping our word, and we will fight for every vote.”

According to an Ohio tally by the Associated Press at 3:30 a.m., Mr. Bush had 2,764,809 votes, while Mr. Kerry had 2,620,594.

In the nationwide popular vote, Mr. Bush was ahead with 55,601,359 votes, or 51%, to 51,828,044, or 48%, for Mr. Kerry, according to AP. All the other candidates, including the consumer advocate Ralph Nader, totaled fewer than 1 million votes.

Turnout was reported to be 10 or more percentage points above normal for a presidential election.

Early this evening, exit polls buoyed the spirits of Mr. Kerry’s aides, but as the night wore on they looked increasingly glum. Mr. Bush’s supporters were downbeat early on, but became more ebullient as the hours went by. The president’s election-night party in Washington erupted in cheers as networks began to call Ohio for the incumbent.

At that point, Mr. Kerry’s senior aides suddenly grew scarce at the filing center in Boston, where they mingled with reporters earlier in the night.

In voting across the country yesterday, there were few surprises, with most states following the same course as in the 2000 election.

New Hampshire and its four electoral votes, however, appeared to be headed into Mr. Kerry’s column. In early tallies, Nevada, which has five electoral votes, was also leaning narrowly in Mr. Kerry’s direction. Both states backed Mr. Bush four years ago.

Mr. Bush began his day by voting near his home at Crawford, Tex., accompanied by his wife, Laura. He then flew unusual invitation to the residential quarters. There they saw Mr. Bush sitting on a couch, watching election returns along with members of his family, including his father, and his dog, Barney.

In response to a question, the president said he was “very upbeat” about his chances to keep his job for another four years.

“I believe I will win, thank you very much,” he told reporters.

“I feel good about it, I’m glad to be watching the returns here with my family and friends,” Mr. Bush said. “It’s going to be an exciting evening.” He said he was convinced his victory would be sealed before the night was out.

In a jocular mood, the president noticed his dog was eyeing the reporters, “Barney, you have something to say?” he asked, chuckling.

Top presidential aides were gathered in the Roosevelt Room, including the chief of staff, Andrew Card, the national security adviser, Condoleezza Rice, the communications director, Dan Bartlett, and the counselor, Karen Hughes.

An adviser to Mr. Kerry, Joseph Lockhart, told reporters the senator had no plans to counter Mr. Bush’s appearance.

“There was great picture,” Mr. Lockhart said, but we think when the votes are counted and the spin is put aside, we’re going to be in very strong shape.”

The Clinton White House press secretary said Mr. Kerry had been boosted by large turnout among young voters. “This is the year that it actually happened,” Mr. Lockhart said.

Exit polls, however, did not bear that out. Voters ages 18 to 29 were said to have accounted for 17% of all voters, the same proportion as in 2000. There was some indication, though, that in certain swing states, such as Ohio, young voters did turn out in greater numbers.

Mr. Lockhart said Mr. Kerry’s team was not worried that he was trailing in early returns from Ohio.

“When you see the southern part of the state where Democrats are strongest really come in, you’ll see our margin of victory,” he said.

About 10,000 supporters of Mr. Kerry gathered in Copley Plaza to await the election results and a late-night speech from the senator.

Aides to both candidates said the two men were likely to be slow to claim victory or concede defeat. In 2000, Vice President Gore called Mr. Bush to concede but withdrew the concession after it became clear that results of the vote in Florida were in dispute.