President-elect Joe Biden addressed a deeply divided nation Saturday night, turning to the challenges ahead by grounding his victory speech in the spirit of compromise, asking supporters of President Donald Trump to give him a chance, and calling on all Americans to turn the page from what he described as a "grim era of demonization."

Biden made that plea for unity and understanding in his home town of Wilmington, Delaware, at an extraordinary moment in American history when the current occupant of the White House showed no indication that he plans to concede to his rival and continued to push the fiction on Twitter that he had won the election, while making baseless accusations about how the election was stolen from him.

After jogging on stage wearing a mask, Biden repeated his promise that he would seek to unify rather than divide. He pledged to govern by the creed that he does not see blue states and red states, but only the United States.

When the campaign started nearly two years ago, it would have been extraordinary to think that Americans would show up to a victory rally wearing masks. The fact that they had to, and at a drive-in event outside in November, was a reminder of the moment of national extremis that Biden and Harris will inherit in January.

Biden noted that he sought the nation's highest office “to rebuild the soul of America, to rebuild the backbone of this nation, the middle class and to make America respected around the world again.” He acknowledged how Black voters carried him across the finish line both in the primary and then again in the general election by the increasing turnout in key battleground states.

But it was Biden's entreaties to Trump voters, who also turned out in huge numbers on Election Day, that were the most striking as he faces the daunting task of governing in a sharply polarized nation.

“For all those of you who voted for President Trump, I understand the disappointment tonight. I've lost a couple of times myself. But now, let's give each other a chance,” Biden said. “It's time to put away the harsh rhetoric, lower the temperature, see each other again, listen to each other again. And to make progress we have to stop treating our opponents as enemies.”

Alluding to scripture, he added: “This is the time to heal in America.”

The speech marked the time-honoured pivot between a hard-fought campaign and the calls for unity that are traditional after an acrimonious election. It also epitomized the perceptible start of the process of shifting of power to a newly elected president from a defeated one, who scorned tradition at every turn. And it was a rare moment in the last five years that Trump was not the dominant figure seizing the attention on the national political stage.

Cognizant of the historical import of the moment, the Biden campaign opened the event by having Vice President-elect Kamala Harris introduce her running mate. Harris will be the first woman — and the first woman of colour — to serve as vice president.

Invoking the legacy of the late Georgia Congressman John Lewis, Harris praised the campaign's supporters for turning out in record numbers at a time when “our very democracy was on the ballot in this election,” and said they had chosen hope, science and truth by selecting Biden as the next president.

She also credited Biden for having the “audacity to break one of the most substantial barriers that exist in our country and select a woman as his vice president.”

“While I may be the first woman in this office, I will not be the last, because every little girl watching tonight sees that this is a country of possibilities.”

“And to the children of our country, regardless of your gender, our country has sent you a clear message: Dream with ambition, lead with conviction, and see yourself in a way that others might not see you, simply because they've never seen it before. And we will applaud you every step of the way.”

As Biden and Harris prepared for those victory speeches, jubilant celebrations erupted in big cities across America, with supporters pouring into the streets — shouting, chanting, singing, dancing and waving flags as drivers honked their horns — to mark the victory and the end of Trump's presidency.

The celebrations began near the White House on Saturday while Trump was golfing in Virginia — forcing the smouldering President to wind his way back to 1600 Pennsylvania Avenue in his motorcade through those crowds after hitting the links. There was no sign that Trump would extend the traditional invitation for a White House visit to the President-elect as he continues to falsely maintain that the election was stolen from him.