Joe Biden says he is on course to win a "clear majority" in the US presidential election and take most of the remaining battleground states to push him above 300 Electoral College votes.
As counting continues in a series of nail-biting races, the Democratic candidate claimed he had already got a "mandate for action", seeking to pile pressure on Donald Trump to concede.
He admitted the process of calling a result "moves very slow" but urged for an end to "partisan warfare", urging Americans to "remain calm, patient and let the process work out".
Mr Biden is leading in four of the six states yet to declare - Arizona, Georgia, Nevada and Pennsylvania.
He only needs the latter's 20 Electoral College votes to add to his existing 253 to push him over the 270 line that will guarantee him the keys to the White House.
But Mr Trump, who is ahead in North Carolina and Alaska, is ramping up unsubstantiated and contested claims the election was rigged against him.
"I had such a big lead in all of these states late into election night, only to see the leads miraculously disappear as the days went by," he tweeted.
"Perhaps these leads will return as our legal proceedings move forward!"
Senior Republicans have stepped in to warn that the baseless allegations of mass fraud will lead to "destructive and dangerous passions" running high, and urged for vote counting to continue.
Election administrators are ploughing on with tallying up results.
In some states they are having to wait for deadlines for mail-in ballots and those from overseas voters to reach them before declaring a final result, because the margins are razor-thin.
But Mr Biden has tried to present himself as the president-elect - a term already used to describe him by the most senior Democrat in Congress, Nancy Pelosi.
Speaking from his home state of Delaware late on Friday night, the former senator pointed to how he had leapfrogged Mr Trump to take the lead in some states.
"We're going to win this race with a clear majority, with the nation behind us," he predicted.
Winning the most votes of any presidential candidate ever also gave him a "mandate for action on COVID, the economy, climate change and systemic racism", Mr Biden added.
And striking a reconciliatory tone following protests outside some counting centres by supporters of Mr Trump, he said: "We don't have any more time to waste on partisan warfare."
The speech sparked some cheers from the crowd, but shouted questions from journalists went unanswered.
Meanwhile the president is holed up in the White House, where his chief-of-staff has tested positive for coronavirus.
Mark Meadows frequently appeared at public events without wearing a face covering - including the Mr Trump's election night party.
It was there in the early hours of Wednesday that Mr Trump first tried to undermine the result and vowed to take his fight to the Supreme Court.
While a recount gets under way in Georgia, a local Republican official there overseeing the count, Gabriel Sterling, said "we're not seeing any widespread irregularities".
And the Democrat mayor of Philadelphia in Pennsylvania Jim Kenny, told Sky News: "What the president needs to do is put his big boy pants on, he needs to acknowledge the fact that he lost and he needs to congratulate the winner."
Prime Minister Boris Johnson has tried not to wade into the row about the legitimacy of the election.
But he said he has "every confidence" in the checks and balances of the US system and promised to "work closely" with whoever wins.
Analysis: Already a sense the Biden era has begun
By Greg Milam, US correspondent
If it wasn't the victory speech that Joe Biden had hoped to deliver to the American people at primetime on a Friday night, it was certainly a striking proclamation of the very different direction he is offering the country.
The soon-to-be president-elect, standing alongside his vice presidential pick Kamala Harris, had been expected to merely provide a progress report on the state of the slow march to an election result.
Instead, on COVID-19, the economy, climate change and the divisions in society, he offered the American people a real glimpse of what they can expect from his administration.
We have heard much of it before, on the campaign trail and since Election Night, but the Biden-Harris project is now looking like it will be a reality for the American people come January.
He mentioned Donald Trump by name just once - to boast about the vote margin - but there was no mistaking his belief that America has spent four years on the wrong path.
If the verbal stumbles and uncertainties that are part of the Biden package were sometimes noticeable, there was no mistaking his belief in what the country needs right now.
He did what presidents usually do: Faced up to the crises gripping the country, empathised with the victims and promised to work towards a way out.
The intent was clear: To project himself as the president-in- waiting, filling the vacuum left by the current occupant of the White House, as he spends his time ranting and raving about the election result.
Who wouldn't agree with Biden's call for the vitriol to be taken out of political and social discourse? It is an easy call to make but, in today's America, a very different proposition to deliver.
The reality is that there are thousands of supporters of Donald Trump who are unwilling to even accept that Biden will be a legitimate president.
They are making their views plain and many of them are determined to hound Biden in office just as they believe the current president has been unfairly attacked by his political opponents.
No-one is going to heal those divisions overnight. We can only hope that Biden is true to his word that he is serious about bridging the divide.
Even before the result has been declared, there is a sense that the Biden era has already begun.