Joe Biden has won the most votes of any presidential candidate in US election history, surpassing the total Barack Obama achieved in 2008.
As of Thursday morning, and with a number of states still to call, Biden has a running total of 72,131,882, according to the Associated Press.
President Obama won in 2008 with 69,498,516, which was the highest ever recorded.
Late night counts in Michigan and Wisconsin has given Biden projected victories in those two states.
Hundreds of thousands of votes are also outstanding in Pennsylvania.
Opinion polls had given Biden a strong lead nationwide for months, but they had shown closer races in battleground states, and the vote did not produce the stinging verdict against the Republican president that the Biden camp had hoped for.
Biden, 77, said in the early hours he was nonetheless confident of winning once the votes are counted, and urged patience.
Trump, 74, appeared at the White House soon after to declare victory.
“We were getting ready to win this election. Frankly, we did win this election,” he said, before launching an extraordinary attack on the electoral process by a sitting president.
“This is a major fraud on our nation. We want the law to be used in a proper manner. So we’ll be going to the US Supreme Court. We want all voting to stop.”
Trump provided no evidence to back up his claim of fraud and did not explain how he would fight the results at the Supreme Court, which does not hear direct challenges.
In a tweet, Trump also claimed it was “VERY STRANGE” that later vote counts were skewing towards Biden despite it being well-known for months that this would be the case due to Democrats being less willing to risk visiting crowded polling locations during the coronavirus pandemic.
Voting concluded as scheduled on Tuesday night, but many states routinely take days to finish counting ballots.
Huge numbers of people voted by mail because of the pandemic, making it likely the count will take longer than usual.