Donald Trump is "alive and kicking" as he prepares to launch legal action to stop some counts and challenge results in key battlegrounds he is projected to lose, his team has said.
The US president's campaign manager gave an update on their tactics and claimed Americans had lost faith in democracy.
The incumbent Republican is ahead in Georgia, North Carolina and Pennsylvania while Mr Biden is leading in Arizona and Nevada.
But as the ballots are counted in batches, those razor-thin margins could narrow further, or see one candidate overtake the other.
The momentum seems to be behind Mr Biden, who is winning the popular vote and within touching distance of the 270 Electoral College votes needed to guarantee the presidency, on 253.
Mr Trump currently has 214 Electoral College votes.
He had demanded election administrators "stop the count" in Arizona, Nevada, Pennsylvania and Georgia, and has claimed a "big legal win" after his campaign said they got a court order in Philadelphia to enter a count to observe it.
"All of the recent Biden claimed states will be legally challenged by us for voter fraud and state election fraud," he vowed in a tweet, again without providing evidence.
In Nevada, his campaign declared at a news conference that "the system is corrupt".
They presented one resident - Jill Stoke - who claimed she had been the victim of voter fraud and another who said he was denied access to watch ballots being counted, but they all refused to take questions or verify those accounts.
A registrar later said that contrary to Ms Stoke's claims, she had actually already voted and then tried to vote again.
The Trump campaign has also lost a legal bid to halt counting in Michigan - a state the Republicans are already projected to lose and where 99% of votes have been counted.
Mr Biden's team has dismissed claims of wide-scale fraud as "baseless" and "political theatre".
One adviser, Bob Bauer, said: "It is to create an opportunity to message falsely about what is taking place in the electoral process... This is part of a broader misinformation campaign."
Urging patience, Georgia's election system manager Gabriel Sterling said people should stay calm and wait for officials to finish doing their job.
"Fast is great and we appreciate fast; we more appreciate accuracy," he said.
"Accuracy is going to be the bedrock upon which people will believe the outcomes of this election, be they on the winning side or the losing side."
A result there is expected to be announced later on Thursday, but could be delayed further if it goes to a recount.
In Nevada, more results are not expected until Friday.
Mr Biden's best chance of victory is flipping the high-value target of Pennsylvania, where the secretary of state is due to make an announcement at 10:15pm (5:15pm Eastern Time).
If he can do that then he will take its 20 Electoral College votes, surpassing the 270 threshold needed without having to rely on the other remaining races.