Donald Trump accepted congratulations from across the political spectrum at home and from leaders around the globe Wednesday, just hours after voters elected him the nation’s 45th president, and he hunkered down in New York to ponder a list of hefty decisions awaiting him.

His victory was cemented by wins in Wisconsin, Pennsylvania and perhaps Michigan — territory the Republican Party hasn’t claimed since the 1980s — defying the pundits and hinting at a political resurgence of white working-class voters who feel neglected by Washington.

Hillary Clinton had been seeking to make history as the first woman to win the White House, but instead the 70-year-old Mr. Trump made history of another sort, becoming the first person elected to the top job without having held a high government office or military command.

Mrs. Clinton and President Obama asked their supporters to accept the results of the election.

Mr. Obama also invited Mr. Trump to the White House on Thursday for an initial meeting to work out the transfer of power. The outgoing chief executive promised his successor the same gracious treatment that he received from President George W. Bush in 2001.

Financial markets, which dipped as the election dragged on Tuesday night, rebounded Wednesday as the first day of Mr. Trump as president-elect went off without a hitch, and as calls for unity abounded.

The president-elect led the way, promising to listen to supporters and opponents alike.

“Now it’s time for America to bind the wounds of division,” Mr. Trump said in his postelection speech early Wednesday. “I pledge to every citizen of our land that I will be president for all Americans.”

As of Wednesday evening, Mr. Trump was projected to have 279 electoral votes, putting him over the 270-vote threshold with Michigan, Arizona and New Hampshire races still to be called. The Republican held leads in the two larger states, which could be worth an additional 27 Electoral College votes.

The president-elect spent the day meeting with Vice President-elect Mike Pence and their staffs at Trump Tower in New York, a building now under heavy protection from the U.S. Secret Service.

On tap for Mr. Trump are a series of tough decisions including whom to name for the vacant Supreme Court seat, how to constitute his Cabinet, what his inauguration party will look like and what sort of agenda he wants to pursue.

Kellyanne Conway, Mr. Trump’s campaign manager, said the results of the election give Mr. Trump “quite a mandate” for that agenda.

Republican leaders on Capitol Hill said they would talk with Mr. Trump about issues to tackle next year. Repealing Obamacare and attempting a massive overhaul of the tax code were areas where they showed some agreement.

Dead, at least for this year, is the Trans-Pacific Partnership, the massive trade deal that Mr. Obama negotiated and hoped to make a capstone during his eight-year legacy. Now much of Mr. Obama’s legacy, achieved through executive action rather than working with Congress, is imperiled.

Mr. Trump could gut the president’s global warming promises, end his deportation amnesty and reverse his efforts to close the prison at Guantanamo Bay, all without a single action by Congress.

Conservative health care advisers laid out a road map for Mr. Trump to neuter Obamacare on his first day in office, saying he can suspend payments to insurance companies, making it clear that they won’t be able to stay afloat through the government’s largesse.

Democrats sought to constrain the significance of Mr. Trump’s election, saying the results weren’t decisive — particularly with Mrs. Clinton on track to win the popular vote.

A number of liberal leaders said the forces that propelled Mr. Trump were the same ones Democrats were trying to harness, such as punishing the wealthy to reduce income inequality.

“Donald Trump tapped into the anger of a declining middle class,” said Sen. Bernard Sanders, the Vermont independent who challenged Mrs. Clinton in the Democratic primary.

“People are tired of working longer hours for lower wages, of seeing decent-paying jobs go to China and other low-wage countries, of billionaires not paying any federal income taxes and of not being able to afford a college education for their kids — all while the very rich become much richer,” Mr. Sanders said.

Both Mr. Obama and Mrs. Clinton said Mr. Trump had earned the right to lead.

“We owe him an open mind,” Mrs. Clinton said in a speech publicly conceding the election.

But she and Mr. Obama also chided Mr. Trump, saying he needs to moderate the tone he used and the policies he promoted during the campaign.

“Our constitutional democracy enshrines the peaceful transfer of power, and we don’t just respect that; we cherish it,” Mrs. Clinton said. “It also enshrines other things — the rule of law, the principle that we are all equal in rights and dignity, freedom of worship and expression. We respect and cherish these values too, and we must defend them.”

Liberal groups weren’t so willing to accept the results in good faith.

“Last night, racism won,” the Center for American Progress Action Fund, the political arm of the think tank created by Mrs. Clinton’s campaign manager, said in its daily memo.

The different reactions between Democratic officeholders and liberal pressure groups could be a problem for moving the party forward. They appear to face many of the same obstacles the Republican Party has struggled with since the emergence of its tea party right wing in recent years.

House Minority Leader Nancy Pelosi of California, who is likely to keep her post in the next Congress, said Democrats might be able to find common ground with Mr. Trump on rebuilding American infrastructure.

In Tuesday’s voting, Mr. Trump flipped a number of states that Mr. Obama won in 2008 and 2012 and rebuilt most of the coalition that powered George W. Bush to wins in 2000 and 2004. He added Wisconsin and Pennsylvania to the Republican tally but ceded Virginia, which went Democratic for the third straight election.

The map turned out to be surprisingly close to what Mr. Trump had predicted over the past few months, with Republicans proving competitive in Rust Belt and Midwestern states where he said the Obama economy was failing.

Exit polls also proved to be drastically off base Tuesday, predicting Mrs. Clinton and Democratic Senate candidates would win races that they ended up losing by wide margins.

Analysts said Mr. Trump’s message resonated with white voters across the country who felt ignored by Washington politicians and turned out en masse to make themselves heard.

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