Election 2020 updates: Biden warns of 'dark winter,' pushes masks in pandemic plan

ABC News projects Biden will win the battleground state of Nevada.

Former President Barack Obama "spoke separately this afternoon with president-elect Joe Biden and vice president-elect Kamala Harris," an Obama spokesperson said. "He congratulated them on their historic victory and told them how proud he was of the campaign they ran in unprecedented times.”

Obama said in a statement Saturday that he "couldn't be prouder" of Biden and Harris.

"We’re fortunate that Joe’s got what it takes to be President and already carries himself that way. Because 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.

"I know he’ll do the job with the best interests of every American at heart, whether or not he had their vote. So I encourage every American to give him a chance and lend him your support. The election results at every level show that the country remains deeply and bitterly divided," he said.

"Our democracy needs all of us more than ever," Obama said. "And Michelle and I look forward to supporting our next President and First Lady however we can."

Former President Jimmy Carter said in a statement, "Rosalynn joins me in congratulating our friends President-elect Joe Biden and Vice President-elect Kamala Harris. We are proud of their well-run campaign and look forward to seeing the positive change they bring to our nation."

Former President Bill Clinton tweeted, "America has spoken and democracy has won. Now we have a President-Elect and Vice President-Elect who will serve all of us and bring us all together. Congratulations to Joe Biden and Kamala Harris on your momentous victory!

Trump’s lawyer, Rudy Giuliani, on Saturday vowed to file a lawsuit Monday to challenge the conduct of elections officials in Pennsylvania.

In comments laced with vague and unfounded allegations of voter fraud in Pennsylvania, Giuliani alleged that the Trump campaign was deprived of the ability to watch the ballots being processed. And he said the campaign would make similar allegations in other states that could lead the campaign to make the case a “massive nation-wide lawsuit.”

“We were deprived of the right to inspect if a single one of those ballots is legitimate,” Giuliani said. “That is unheard of, it’s illegal, it’s unconstitutional, and we will be bringing an action challenging that.”

The Trump campaign has now brought multiple similar charges into court since Election Day and all but one of the cases has been rejected – in Michigan and Nevada. In Pennsylvania, a state judge ordered election officials to allow observers to move closer to poll workers, but a federal judge refused to halt the count based on the claims.

In several of the cases, judges have used strikingly similar language to criticize Trump campaign attorneys for bringing the cases without sufficient evidence. Biden attorney Bob Bauer on Thursday called the lawsuits "meritless."

Observers are permitted to watch the processing of ballots in most states, including Pennsylvania, but not allowed to intervene as the ballots are processed. They can note any irregularities and report them back to their campaign’s legal team.

Giuliani alleged that Trump campaign representatives were not close enough to see if ballots had errors or irregularities. But for days, Trump campaign officials have not been able to explain what remedy they could expect should a court agree that they were not given sufficient access to watch the poll workers open envelopes of mail-in ballots and inspect them to make sure signatures match, dates are accurate, and the secrecy envelope is used properly.

-ABC News' Matt Mosk and Alex Hosenball

Trump, who is golfing on Saturday, released a defiant statement through his campaign, claiming, "this election is far from over."

Trump blasted Biden for "rushing to falsely pose as the winner."

Following media projections, Biden changed his Twitter bio to "President-elect." Biden said in a statement Saturday, "I am honored and humbled by the trust the American people have placed in me."

Trump also touted the coming legal fight.

"Beginning Monday, our campaign will start prosecuting our case in court to ensure election laws are fully upheld and the rightful winner is seated," he said. "The American People are entitled to an honest election: that means counting all legal ballots, and not counting any illegal ballots."

The president again pushed unfounded claims that "Only a party engaged in wrongdoing would unlawfully keep observers out of the count room – and then fight in court to block their access."

Asked if Trump would call Biden to concede, White House deputy press secretary Judd Deere said: “No scheduling updates. The campaign has released a statement from the president.”