WASHINGTON

Emboldened Republicans claimed a mandate Wednesday for Donald Trump after his stunning election as the 45th president of the United States.

With results too close to call Tuesday night in several key battleground states, many people went to bed not knowing the election’s outcome. But news reports broke about 2:45 a.m. Wednesday that Democrat Hillary Clinton had telephoned her Republican opponent to concede, acknowledging that he had garnered the required 270 electoral college votes to clinch the presidency.

Mr. Trump then took the stage about 3 a.m. to address hundreds of his jubilant supporters waiting at a victory rally in Manhattan. He said it was “time for America to bind the wounds of division.”

“I pledge to every citizen of our land that I will be president for all Americans,” he said.

It was an astonishing victory for the 70-year-old celebrity businessman and political novice who capitalized on voters’ economic anxieties, took advantage of racial tensions and overcame a string of sexual assault allegations during a hard-fought battle to win the White House.

Mrs. Clinton, a former U.S. secretary of state and U.S. senator representing New York, told crestfallen supporters in a late-morning address Wednesday that the GOP victor deserved a “chance to lead.”

President Obama pledged a smooth transition of power.

“We are now all rooting for his success in uniting and leading the country,” President Obama said of the man who spent years questioning President Obama’s birthplace and challenging the legitimacy of his presidency.

President Obama, who had declared Mr. Trump unfit for the presidency, invited him to the White House on Thursday.

Mrs. Clinton’s emotions were raw as she addressed a crowd of supporters, eyes wet with tears, who gathered in a New York ballroom late Wednesday morning where she conceded the election.

Joined by her husband, former President Bill Clinton, and daughter Chelsea, Mrs. Clinton was introduced by her vice presidential running mate, U.S. Sen. Tim Kaine of Richmond.

“I’m proud of Hillary Clinton because, in the words of Langston Hughes, she has held fast to dreams,” Sen. Kaine said, his eyes filled with tears. His wife, Anne Holton, the former Virginia secretary of education, was by his side. “She’s been in battles before where, if it didn’t go her way, she accepted it but then woke up the next day and battled again for the dreams that she’s held fast to.

“I’ll just say this: Hillary and I know well the wisdom in the words of William Faulkner. He said, ‘They kilt us, but they ain’t whupped us yet,’ ” he said to the applause of the crowd. “We know that work remains. We know that the dreams of empowering families and children remain … It is so comforting, even at a tough time, to know that Hillary Clinton is somebody, until her very last breath, who’s going to be battling for the values that make this nation great and the values that we care so deeply about.”

Taking the stage, with a row of American flags in the background, Mrs. Clinton said the crushing loss was “painful and it will be for a long time.”

She acknowledged that the election showed the nation was “more divided than we thought.”

Still, Mrs. Clinton was gracious in defeat, declaring that “Donald Trump is going to be our president. We owe him an open mind and the chance to lead.”

With several million votes still to be counted, Mrs. Clinton held a narrow lead in the nationwide popular vote. Most of the outstanding votes appeared to be in Democratic-leaning states, with the biggest chunk in California, a state Clinton overwhelmingly won. With almost 125 million votes counted, The Associated Press tally had Mrs. Clinton with 47.7 percent and Mr. Trump with 47.5 percent.

Mr. Trump was uncharacteristically quiet in the aftermath of his triumph and made no public appearances Wednesday. He huddled with jubilant, sleep-deprived advisers at his eponymous skyscraper in Manhattan, beginning the daunting task of setting up an administration that will take power in just over two months. He also met with Vice President-elect Mike Pence and took calls from supporters, family and friends, according to spokeswoman Hope Hicks.

In Washington, Mr. Trump’s scant transition team sprang into action, culling through personnel lists for top jobs and working through handover plans for government agencies. A person familiar with the transition operations said the personnel process was still in its early stages, but the president-elect’s team was putting a premium on quickly filling key national security posts.

According to an organizational chart for the transition obtained by The Associated Press, Mr. Trump was relying on experienced hands to help form his administration. National security planning was being led by former Michigan Rep. Mike Rogers, who previously worked for the FBI. Domestic issues were being handled by Ken Blackwell, a former Cincinnati mayor and Ohio secretary of state.

Mr. Trump was expected to consider several loyal supporters for top jobs, including former New York Mayor Rudy Giuliani for attorney general or national security adviser and campaign finance chairman Steve Mnuchin for treasury secretary. Former House Speaker Newt Gingrich and Tennessee Sen. Bob Corker were also expected to be under consideration for foreign policy posts.

After struggling for months with Mr. Trump’s takeover of their party, Republican leaders embraced the businessman in victory. House Speaker Paul Ryan, who was lukewarm in his support throughout the campaign, praised Mr. Trump for pulling off “the most incredible political feat I have seen in my lifetime.”

“He just earned a mandate,” Speaker Ryan declared.

Indeed, Mr. Trump will take office on Jan. 20, with Congress fully in his party’s control, giving him strength to try to pass his agenda and turn the U.S. Supreme Court in a conservative direction. Even Republicans were stunned by the scope of their electoral success, including many who had been privately predicting Mr. Trump’s defeat.

Mr. Trump’s sweep of the battleground states that decided the election was commanding. He carried Florida, Ohio and North Carolina, three of the election’s biggest prizes, and snatched reliably Democratic Pennsylvania and Wisconsin away from Mrs. Clinton.

In Virginia, the election was a nail-biter, with Mr. Trump in the lead until the Democratic-rich Northern Virginia areas reported their results. Unofficial results in Virginia show Mrs. Clinton winning 1,916,019 votes, or 49.5 percent, to Mr. Trump’s 1,729,448 votes, or 44.68 percent.

Richmond, Petersburg and Henrico County all delivered wins to the Clinton-Kaine ticket. The Democrats won 78.2 percent of the votes for president in Richmond, 87.2 percent in Petersburg and 57.4 percent in Henrico.

Mr. Trump won 48.4 percent of the votes in Chesterfield compared to 46.1 percent for Mrs. Clinton. In Hanover, Mr. Trump won 63.1 percent of the vote compared to 30.9 percent for Mrs. Clinton.

Nationally, Mr. Trump’s support skewed older, male and overwhelmingly white. His supporters said they were deeply dissatisfied with the federal government and eager for change, according to exit polls conducted by Edison Research for The Associated Press and television networks.

If Mr. Trump makes good on his campaign promises, the nation stands on the brink of sweeping change in domestic and foreign policy. He has pledged to repeal President Obama’s signature health care law and pull out of the landmark nuclear accord with Iran. He also vowed to build a wall along the U.S.-Mexico border and temporarily ban immigration from nations with terrorist ties.

Global stock markets and U.S. stock futures plunged early Wednesday on word of Mr. Trump’s election, but later recovered. The Dow Jones industrial average rose 1.4 percent for the day in trading in New York.

It’s unclear whether Mr. Trump, a highly unusual candidate, will embrace many of the traditions of the presidency. He’ll enter the White House owning his own private jet, as well as a hotel just blocks away on Pennsylvania Avenue. He never allowed journalists to fly on his plane during the campaign, as is customary for White House nominees.

Issues of transparency bubbled up right from the start. On Wednesday evening, Mr. Trump’s aides said they would not bring the press corps to Washington with the president-elect for his meeting with President Obama, breaking long-standing protocol.

World leaders congratulated Mr. Trump on his victory. Russian President Vladimir Putin was among the first to reach out. Mr. Trump praised President Putin throughout the campaign and advocated a closer relationship with Russia, despite Moscow’s provocations in Ukraine and elsewhere.

U.S. intelligence agencies have accused Russia of hacking Democratic organizations during the campaign, actions Mrs. Clinton’s team saw as an indication that President Putin was trying to meddle in the election. Mr. Trump notably did not accept the conclusions of intelligence officials.

Before he takes the oath of office, Mr. Trump is to testify in his defense in a Trump University federal class action lawsuit set to begin Nov. 28 in San Diego, Calif., The president-elect is expected to face questioning about his venture’s marketing practices.

The trial will bring Mr. Trump face to face with U.S. District Court Judge Gonzalo Curiel. During the campaign, Mr. Trump triggered widespread outrage by arguing that Judge Curiel’s Latino heritage made the judge irredeemably biased against him. Mr. Trump also called the judge “Mexican” and “Spanish.” Judge Curiel was born in Indiana.