WASHINGTON – Celebrating a momentous election victory that stunned foes and surprised some supporters, President Bush promised yesterday to “serve all Americans” and appealed for the backing of Democrats, pledging to earn their respect in a “season of hope.”

Mr. Bush’s remarks in a victory speech before a rapturous, flag-waving crowd of hundreds of party faithful in downtown Washington came after his rival, Senator Kerry, spared America days of wrenching uncertainty and the rancor of a drawn-out recount in Ohio by conceding defeat.

Last night, unofficial results gave Mr. Bush a record total of 59 million votes, a margin of 3.6 million over the Democrat. With the victor in Iowa, with seven electoral votes, still in question, Mr. Bush had won 279 electoral votes, nine more than the minimum he needed for re-election.

“We had a long night and a great night,” the president said.

“The voters turned out in historic numbers and delivered an historic victory,” Mr. Bush told supporters, who chanted “Four More Years” and stamped their feet as the Bush and Cheney families entered the cavernous hall of the Ronald Reagan Building, a block from the White House.

“America has spoken,” he said, adding that he was “humbled” by the trust and confidence of the voters who gave him a second term.

Looking straight at the cameras, Mr. Bush said: “I want to speak to every person who voted for my opponent. To make this nation stronger and better, I will need your support.”

But the president did not budge from his conservative goals of cutting and simplifying taxes, overhauling Social Security to allow younger workers to privately invest some of their federal withholding in the stock market, and limiting medical-liability awards.

He also promised to “fight this war on terror with every resource of our national power” and offered no doubts about the path he has chosen in Iraq.

Those goals, he said, will require broad backing from Americans, but he seemed to appear to believe that his opponents should move toward his positions, rather than require him to dilute his own policies.

The earlier-than-expected concession from Mr. Kerry allowed Mr. Bush and the Republicans to celebrate a big governing mandate without having to wait for court combat or a prolonging of an election that has been the costliest and one of the most vitriolic in modern American political history.

Mr. Kerry’s decision to concede came in late morning and was triggered by Nevada being called for the president. Also significant in Mr. Kerry’s decision to bring his long campaign to a halt was advice from senior Ohio Democrats. They told the Democratic presidential nominee that counting provisional ballots in Ohio would change nothing and wouldn’t lead to the Buckeye State being switched from the GOP column, a senior Democratic official told The New York Sun.

Mr. Kerry told his crestfallen supporters during his concession speech at Faneuil Hall in Boston, where he launched his bid for the White House a year ago, that there was no point in disputing the result in Ohio.

“In America, it is vital that every vote count …but the outcome should be decided by voters, not a protracted legal fight,” he said.

“We cannot win this election,” the senator said.

At several points Mr. Kerry choked up when delivering his speech, in which he “pledged to bridge the partisan divide.” He remains in the Senate, though his running mate, Senator Edwards, did not seek re-election and is being succeeded by a Republican, Richard Burr.

Mr. Bush will enter his new four-year term in office with strengthened Republican majorities in both houses of Congress and will have the undisputed legitimacy that a momentous popular-vote win brings, top GOP officials said.

He is the first president since his father in 1988 to receive an outright majority in the popular vote, and, as Vice President Cheney noted yesterday in introducing the president at the victory celebrations, he won the greatest number of popular votes ever for a presidential candidate, surpassing the landslide triumphs of conservative icon Ronald Reagan.

According to White House spokesman Scott McClellan, Mr. Kerry was gracious in the phone call he made to the president to inform him of his decision to concede.

Mr. Bush told the Massachusetts senator, “I think you were an admirable, worthy opponent” who waged “one tough campaign.”

“I hope you are proud of the effort you put in. You should be,” Mr. McClellan quoted the president as saying to his vanquished opponent.

Mr. Kerry told his supporters that he and the president had “talked about the danger of division in our country and the need – the desperate need – for unity, for finding common ground and coming together.”

In the immediate aftermath of the election victory, which saw the GOP add four seats to its Senate majority and increase by a half dozen seats its majority in the House, there was talk among lawmakers of the importance of bringing America together. Whether a sense of national unity holds in Washington politics, however, remains in doubt. Few veteran politicians predicted the capital will be less divisive in the months to come.

Some maintained that the Democrats’ frustration at the size of their defeat will bring their anger to a boil. Aside from Mr. Bush’s win there was deep dismay yesterday in Democratic ranks over the toppling of the Senate minority leader, Tom Daschle, who lost his re-election bid in South Dakota by a mere 4,000 votes.

Not all Democrats were happy with the timing of Mr. Kerry’s concession. Some had wanted to continue the election fight. Mr. Edwards urged the Massachusetts senator to delay conceding and, in trial-lawyer style, counseled delay until all options had been fully explored, Democratic sources told the Sun.

In his speech yesterday afternoon in Boston before Mr. Kerry delivered his concession address, Mr. Edwards was combative and sounded as though he were still on the primary trail seeking his party’s nomination for the White House.

Some Democrats were defiant, insisting that Mr. Bush did not have a mandate and arguing that the election result revealed a deeply divided nation still roughly split evenly. They said the political rift had hardly budged since the last presidential election. It was noted that, pending the Iowa result, only two states, New Mexico and New Hampshire, changed hands in this week’s election – assuming Mr. Bush indeed did win New Mexico, which was exceedingly close.

The chairman of the Republican National Committee, Edward Gillespie, disputed talk that the country is split down the middle, maintaining Mr. Bush had pulled off a “decisive win in the popular vote.” He said the country is not “as closely divided as it is made out to be.”

He highlighted the approval in 11 states of constitutional amendments limiting marriage to one man and one woman as evidence that the country is less divided on social issues than the Democrats like to portray it.

For one of the most partisan of Republicans, the House majority leader, Tom DeLay of Texas, this isn’t the time to be talking about compromise. The scale of the GOP sweep provides the president and Capitol Hill Republicans with a mandate for action, he said.

“The American people saw the moral leadership of George Bush and they ratified his leadership and the Republican leaderships in the House and Senate,” Mr. DeLay said.

Veteran Democrats, too, express doubt there will be much conciliation for very long.

“I can tell you that at least in my lifetime, I don’t recall any president so despised by Democrats as they do this guy,” said a former congressman and Clinton chief of staff, Leon Panetta.

The expanded Republican majorities in Congress should strengthen the president’s hand in pushing through legislation and judicial nominations. But the GOP is still short of the votes needed in the Senate to overcome Democratic filibusters, and a former GOP House speaker-elect, Robert Livingston, said he doubts Senate Democrats will be in the mood to work with the president – even with the departure of Mr. Daschle, who was highly effective in blocking moves by the Bush administration.

According to Mr. Livingston, there are no dealmakers in the Democratic caucus able to treat with the GOP and the White House. The disappearance of old-line Southern Democratic senators has left the caucus in the hands of liberals. “There is no one there who can moderate them,” Mr. Livingston told the Sun.

The challenges for Mr. Bush are not only at home, and in his second term his foes overseas may not be the only ones who prove difficult.

Yesterday, in welcoming the re-election of Mr. Bush, Britain’s leader Tony Blair, a staunch ally of the president in the war on terror, served notice that he expects some payback for his backing of the American-led invasion of Iraq.

The prime minister urged the president to use his second term to focus on the Middle East peace process and indicated Mr. Bush needs to repair America’s relations with Europe.