Hillary Clinton conceded defeat to Donald J. Trump yesterday, acknowledging the pain of the defeat in remarks in New York while calling on her supporters to accept that he would be president and to give him a chance to lead with an open mind.

President Obama, speaking in Washington, also said he would work to ensure a smooth transition to a Trump administration and that, despite their differences, we are "all rooting for his success.”

And House Speaker Paul Ryan proclaimed that Trump had achieved a political feat and earned a mandate by reaching new voters.

The Republican leader said he was certain that they would work well together on a conservative policy agenda.

Wiping a tear, Clinton thanked her supporters in her concession speech, and said that she feels pride in the campaign that she ran.

Of Trump, Clinton said she hopes he "will be a successful president for all Americans,” and that she respects and cherishes the peaceful transition of power.

She told her supporters that they must accept that Trump will be president. "We owe him an open mind and a chance to lead,” she said.

After a long campaign, Clinton acknowledged that the loss cuts deep. "This is painful, and it will be for a long time,” she said. She also expressed regret that she did not shatter the glass ceiling, but said, "Someday, someone will and hopefully sooner than we might think right now.”

Clinton said she hopes citizens will still fight for the values that she promoted in her campaign and that "the American dream is big enough for everyone.”

However, she acknowledged that the country was more divided than she realised.

To the women and girls who supported her, Clinton said that "nothing has made me prouder than to be your champion.”

The former secretary of state, like many in her party, entered election day confident in a victory that would have ensured Democrats retained the White House for a third consecutive term.

But Trump, the real estate magnate turned reality television star, demonstrated unexpected strength in Rust Belt states that had been the foundation of President Obama’s two victories.

Possibly facing her last opportunity for a presidential run, Mrs Clinton, 69, acknowledged Tuesday night’s results were painful and that she was disappointed.

She urged her assembled staff and supporters — deflated after recent national opinion polls indicated a good chance at victory — to continue to work for a better nation.

Senator Tim Kaine, the Democratic vice-presidential nominee, who spoke first, said: "I’m proud of Hillary Clinton because she has been and is a great history maker,” pointing to her long career of public service.

He saluted her for winning the popular vote in the election, drawing cheers.

Kaine acknowledged the painful defeat that he and Clinton sustained, but said that the words of William Faulkner gave them hope.

"They killed us but they ain’t whupped us yet,” Kaine said, noting that the work and dreams of empowering children and families remains.

Obama on Trump

Obama said he and former President George W. Bush had major differences eight years ago, but they managed a successful transition.

He expects to do so with Trump, while acknowledging that they have their differences, and he invited the president-elect to come to the White House today.

Obama reminded the country that we "are all on the same team” and characterised politics as an "intramural scrimmage.”

He said he was heartened by the conversation that he had with Trump at 3:30am yesterday and that he hopes he maintains that spirit.

Obama said he was proud of Clinton, who gave her concession speech on Wednesday just before Obama spoke, and called her a historic figure.

Obama said he told his team to "keep their heads” up and he reminded them that they should be proud of all that they have accomplished during his presidency.

Obama called on Americans to move forward with the presumption of good faith in fellow citizens. He said that those who are disappointed should not give up on their dreams.

"Sometimes you lose an argument, sometimes you lose an election,” he said, with Vice President Joe Biden Jr. by his side. "But the path this country has taken has never been a straight line. We zig and zag.

Agencies