Emboldened Republicans claimed a mandate Wednesday for President-elect Donald Trump after his astonishing election triumph, and an emotional Hillary Clinton told crestfallen supporters the GOP victor deserved a “chance to lead.” President Barack Obama pledged a smooth transition of power.

"We are now all rooting for his success in uniting and leading the country,” the president said of the president-elect, the man who spent years questioning Obama's birthplace and challenging the legitimacy of his presidency. Obama, who had declared Trump unfit for the presidency, invited him to the White House Thursday.

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, 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 Trump'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, 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.

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 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 him for pulling off “the most incredible political feat I have seen in my lifetime.”

“He just earned a mandate,” Ryan declared.

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

Clinton's emotions were raw as she addressed a crowd of supporters, eyes wet with tears, who gathered in a New York ballroom. She said the crushing loss was “painful and it will be for a long time” and acknowledged that the nation was “more divided than we thought.”

Still, 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, 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 Clinton with 47.7 percent and Trump with 47.5 percent.

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 Clinton.

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

It's unclear whether 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, Trump aides said they would not bring the press corps to Washington with the president-elect for his meeting with Obama, breaking long-standing protocol. 

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

World leaders congratulated Trump on his victory. Israeli Prime Minister Benjamin Netanyahu, who had a contentious relationship with Obama, called the Republican a “true friend of Israel.” British Prime Minister Theresa May said the US and United Kingdom would remain “strong and close partners on trade, security and defense.”

Russian President Vladimir Putin was among the first to reach out to the incoming American leader. Trump praised Putin throughout the campaign and advocated a closer relationship with Russia, despite Moscow's provocations in Ukraine and elsewhere.

US intelligence agencies have accused Russia of hacking Democratic organizations during the campaign, actions Clinton's team saw as an indication that Putin was trying to meddle in the election. Trump notably did not accept the conclusions of intelligence officials. (AP)