In a tweet issued on Sunday, the president tweeted that “he won”, referring to his Democrat challenger, but claimed, despite any evidence, that the election was "rigged".
He added that Mr Biden’s victory was only “in the eyes” of the media.
Also on Sunday, Mr Trump's lawyer, Rudy Giuliani said the president was "vigorously" contesting the election result in the courts.
Despite Mr Trump's repeated and apparently baseless claims, no evidence suggests the election was not fair, both state and federal officials say the November 3 vote was safe and secure.
On Saturday, police arrested at least 20 people as thousands of Donald Trump supporters rallied behind baseless claims of election fraud.
The “Million Maga March” took place along Washington DC’s Pennsylvania Avenue from Freedom Plaza, near the White House.
Mr Biden defeated his rival by winning back a trio of mid-western battleground states: Michigan, Wisconsin and Pennsylvania, and topped the 270 electoral vote threshold to clinch the presidency.
So far, Mr Biden has 77.5 million votes, the most ever by a winning candidate, to Mr Trump’s 72.3 million - the second highest number of votes ever recorded.
The president has previously refused to accept the results of the election and he dug in again on Sunday, saying: “I concede NOTHING! We have a long way to go.”
Even while seemingly acknowledging Mr Biden’s victory, he also argued without evidence that the former vice president only won because the election was “rigged”.
Mr Trump then made unsubstantiated complaints about access for poll watchers and vote tabulations, and asserted “WE WILL WIN!”. Twitter soon posted warning labels about the tweets.
Election officials from both political parties have stated publicly that the election went well and international observers confirmed there were no serious irregularities.
Mr Trump’s campaign has tried to mount legal challenges across the country, but many have been thrown out and none has included any evidence that the outcome might be reversed.
More than a week after election day, Mr Trump has neither called Mr Biden nor made a formal concession, and White House officials have insisted they are preparing for a second term.
In recent days, Mr Trump appeared to be inching closer to acknowledging the reality of his loss.
In comments in the Rose Garden about a coronavirus vaccine on Friday, Mr Trump said his administration would “not be going to a lockdown” to slow the spread of Covid-19, and added that “whatever happens in the future, who knows which administration it will be? I guess time will tell.”
On Sunday, Mr Trump also renewed his groundless attacks on election technology firm Dominion Voting Systems, without evidence of any serious irregularities.
Dominion has said it “denies claims about any vote switching or alleged software issues with our voting systems”.
The Cybersecurity & Infrastructure Security Agency, a federal agency that oversees election security, said in a statement last week the “November 3rd election was the most secure in American history.”
The agency said: “There is no evidence that any voting system deleted or lost votes, changed votes, or was in any way compromised.”
In his latest fundraising email, Trump told supporters that “we are fighting to ensure EVERY SINGLE LEGAL ballot is counted” and that he had “legal teams on the ground in every critical state.”