(CNN) — 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 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-honored 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 color — 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 exists 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.”

On Saturday, 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 smoldering 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.

Trump’s refusal to concede

While Trump has yet to give any public sign he’s prepared to relinquish power, Jared Kushner, the President’s son-in-law and senior adviser, has approached him about conceding the election, two sources tell CNN. First lady Melania Trump has also advised the President that the time has come for him to accept the election loss, a source familiar with the conversations told CNN on Sunday.

Trump has not denied the outcome of the election, privately at least, sources tell CNN, and he returned to the golf course Sunday. But he’s continuing to push his attorneys to pursue legal challenges that would delay formal certification of the results. Chief of staff Mark Meadows, who is working from home after testing positive for coronavirus, has discussed next steps with the legal team.

Trump again on Saturday baselessly impugned mail-in ballots, which overwhelmingly tipped the election in Biden’s favor, and repeated the falsehoods on Twitter that he “WON THE ELECTION.” He claimed “bad things happened” in the election that his poll observers were not allowed to see, even though there is no evidence that GOP poll watchers were systematically shut out of the process anywhere in the country.

“71,000,000 Legal Votes. The most EVER for a sitting President!” Trump tweeted Saturday afternoon. (While the popular vote tally was continuing to rise for both men as ballots were counted Saturday, Biden had won 74.5 million votes and Trump had won 70.4 million votes).

Trump’s campaign team is expected to continue its effort to dispute the election results with a next round of lawsuits Monday, but so far they have been unable to point to any credible instance of voter fraud that would alter the outcome of the race.

“I will not rest until the American People have the honest vote count they deserve and that Democracy demands,” Trump said in a statement Saturday after the race was called.

On Sunday, Biden campaign senior adviser Symone Sanders told CNN’s Jake Tapper on “State of The Union” that “a number of Republicans from the Hill have reached out. I don’t believe anyone from the White House has.”

As the Trump campaign maps out its legal strategy, it is not clear how isolated instances of irregularities, even if found, would add up to a case with sufficient legal questions to make it all the way to the Supreme Court or would challenge the integrity of an election that Biden looks set to eventually win with sufficient electoral votes, which would make challenges in individual states unlikely to alter the national result.

The legal front looks increasingly like a rallying point for partisans keen to prevent Biden’s presidency from being seen as legitimate by Trump supporters and as a face-saving way for the President himself to explain his defeat. Renowned Republican election lawyer Benjamin Ginsberg said that there was no sign that the President had any case that could change the result of the election. He told CNN’s Erin Burnett that there was so far “no evidence of the systemic fraud or irregularities to cast any of the results in any of the states into doubt.”

While Trump may not accept that he has lost, many world leaders did on Saturday as they sent congratulatory messages to Biden and Harris.

In a sign of how quickly global realities shift after a US election, even some leaders who had courted Trump, including British Prime Minister Boris Johnson, rushed to congratulate the President-elect.

In perhaps the most notable message, India’s nationalist Prime Minister Narendra Modi, who had appeared at huge campaign-style rallies with Trump in India and the United States, tweeted a picture of Biden leaning in to whisper in his ear during a previous meeting. Modi sent a separate tweet congratulating Harris and noting her Indian heritage, saying her success was a great source of pride for Indian Americans and her “chittis” — a Tamil term of endearment that has been used by the vice president-elect.

A complex governing challenge ahead

Many prominent Republicans remained silent this weekend, but there were a few exceptions, including former President George W. Bush — who won the presidency in 2000 after the contentious Florida recount — and Utah Sen. Mitt Romney, the 2012 Republican nominee who has often sparred with the President. Trump’s failure to concede and congratulate his opponent may have suppressed normal courtesies from Republican leaders who remain intimidated by him and dependent on the President’s base for their reelection prospects in 2024. Bush said he had called both Biden and Harris to offer his congratulations.

“Though we have political differences, I know Joe Biden to be a good man, who has won his opportunity to lead and unify our country,” Bush said in a statement Sunday, adding that the fact that Trump won more than 70 million votes was “an extraordinary political achievement.”

“President Trump has the right to request recounts and pursue legal challenges, and any unresolved issues will be properly adjudicated,” Bush said, but added, “The American people can have confidence that this election was fundamentally fair, its integrity will be upheld, and its outcome is clear.”

Romney told Tapper on “State of the Union” that “given the fact that the statisticians have come to a conclusion at this stage, I think we get behind the new President.” When asked whether he had concerns about Trump’s lies about the integrity of the election, the Utah senator noted that “you’re not going to change the nature of President Trump in these last days.”

“He has a relatively relaxed relationship with the truth. And so he’s going to keep on fighting until the very end,” Romney said. “But I’m convinced that, once all remedies have been exhausted, if those are exhausted in a way that’s not favorable to him, he will accept the inevitable. But don’t expect him to go quietly in the night. That’s not how he operates.”

Though Biden pulled off an impressive feat by dispatching an incumbent President and rebuilding the Democrats’ “blue wall” in the Midwest, he is keenly aware of the enormous governing challenge facing him given his slender margin of victory in key swing states. Beyond that — despite fervent hopes that they could deliver a sharp repudiation of Trump and his party at the polls — Democrats actually lost seats in the US House, though they will maintain a majority. Despite massive fundraising, Democrats also failed to make much of a dent in the GOP-controlled Senate. The balance of power in the chamber hinges on two likely runoff elections in Georgia in January.

Biden outlined ambitious goals during his campaign — from a major revamp of the tax code to aggressive efforts to deal with the climate crisis to an expansion of Obamacare — as he tried to hold his fractious party together and inspire the loyalty of progressive Democrats who backed Vermont Sen. Bernie Sanders.

But the political reality of a still-polarized nation, a divided government in Washington and the difficulty of solving the nation’s Covid-19 crisis are likely to temper Biden’s ambitions.

In his remarks Saturday night, Biden promised to get the pandemic “under control” so Americans could reclaim their most precious moments — from visiting with their grandchildren to celebrating weddings and graduations. He noted that he would name a group of leading scientists and experts to his coronavirus task force on Monday, who would build an “action blueprint” that could be deployed as soon as he is inaugurated in January.

The task force will be headed by three co-chairs: former Surgeon General Vivek Murthy, former Food and Drug Administration Commissioner David Kessler and Dr. Marcella Nunez-Smith, an associate professor of medicine and epidemiology at Yale University’s School of Medicine, CNN reported Saturday.

Biden’s plan to tackle the virus, he said, would be rooted in science and constructed out of compassion, empathy and concern. He also plans to take a series of executive actions on day one to reverse some of Trump’s foreign policy actions.

As he did throughout the campaign, Biden spoke Saturday night to the grief that many Americans have experienced during the pandemic, alluding to the loss of his own son Beau Biden, the former attorney general of Delaware who died of brain cancer at the age of 46.

Capturing the faith that sustains him, Biden quoted from a Catholic hymn — “On Eagle’s Wings” — that he said had meant a great deal to his family and to Beau Biden.

“I hope it can provide some comfort and solace to the 230,000 Americans who have lost a loved one to this terrible virus this year. My heart goes out to each and every one of you,” Biden said.

As CNN’s Arlette Saenz reported, there was another reminder of Beau as fireworks lit up the sky outside the Chase Center: One of the songs that played during the show was “A Sky Full of Stars” by Coldplay, one of Beau Biden’s favorite bands.

Former President Barack Obama underscored the challenges ahead for his former vice president on Saturday when he asked Americans to set aside their political differences and “give him a chance and lend him your support.”

“When he walks into the White House in January, he’ll face a series of extraordinary challenges no incoming President ever has — a raging pandemic, an unequal economy and justice system, a democracy at risk, and a climate in peril,” Obama said in a statement. “I know he’ll do the job with the best interests of every American at heart, whether or not he had their vote.”

Obama noted that the election results “at every level show that the country remains deeply and bitterly divided.”

“It will be up to not just Joe and Kamala, but each of us, to do our part — to reach out beyond our comfort zone, to listen to others, to lower the temperature and find some common ground from which to move forward.”

This story has been updated with additional developments Sunday.

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