Joe Biden is the apparent winner of Wisconsin - a key battleground state that would be his first flip from the Republicans.
After a long night of counting, the nail-biting race neared an end as the Democrat challenger was projected to gain its 10 electoral college votes to put him on 237.
That is just 33 short of the required 270 needed to clinch the US presidency.
But Donald Trump's campaign manager has vowed to "immediately" request a recount due to "reports of irregularities" in some counties.
Counting continues meanwhile across several other swing states - with the race to the White House still too close to call.
Mr Biden is ahead in Arizona (11 electoral votes) and Michigan (16), and has already won 69.8 million votes nationwide - a new record for any presidential candidate.
While Mr Trump is leading in Georgia (16), North Carolina (15) and Nevada (6), and has had 66.8 million votes across the country - 3 million more than he achieved last time.
In a bid to derail two potential losses, the Trump campaign has filed lawsuits to try and halt counting in Michigan and Pennsylvania.
They claim their election observers have "not been provided with meaningful access... to observe the opening of ballots" and that there has not been enough "transparency".
Mr Biden failed to make the early breakthroughs he was hoping would hand him a decisive lead on election night.
States like Ohio, Florida, Iowa and Texas remained red, significant tightening the Democrat challenger's options for reaching the prized 270 electoral college votes.
That led to Mr Trump claiming victory and accusing his political opponents of a "fraud on the American public", without evidence.
He used an address to the nation to declare he is taking his fight to the Supreme Court, then fired off a flurry of tweets about the slowly-progressing results in the remaining un-declared states.
"How come every time they count Mail-In ballot dumps they are so devastating in their percentage and power of destruction?" he asked.
In another post, he wrote: "Last night I was leading, often solidly, in many key states, in almost all instances Democrat run and controlled.
"Then, one by one, they started to magically disappear as surprise ballot dumps were counted."
Vote totals are being updated as more votes are counted and there has been no evidence of ballot dumping.
Twitter has had to step in to censor several of the message, warning readers: "Some or all of the content shared in this Tweet is disputed and might be misleading about an election or other civic process."