In the video, Mr Trump is heard continuing to air baseless allegations of election fraud to explain his defeat by Mr Biden despite his attorney general, William Barr, saying on Tuesday that the Justice Department had not uncovered evidence of widespread voter fraud and had seen nothing that would change the outcome of the 2020 presidential election.
Mr Trump has privately told advisers that he is considering a re-election bid but his remarks on Tuesday night are the first time he has said it in public.
“It’s certainly an unusual year. We won an election. But they don’t like that,” Mr Trump told the group, adding: “I call it a rigged election, and I always will.”
The White House has been the site of at least one suspected Covid-19 superspreader event, and dozens of the president’s aides, campaign staffers and allies have tested positive in numerous outbreaks. Mr Trump was hospitalised for the virus in October, and the first lady and two of his sons have tested positive. Numerous others have had to quarantine.
Stephanie Grisham, the first lady’s spokeswoman and chief of staff, said last month that the White House would be moving forward with events “while providing the safest environment possible”.
She said that would include smaller guest lists, that “masks will be required and available, social distancing encouraged while on the White House grounds, and hand sanitiser stations throughout the State Floor.”
“Attending the parties will be a very personal choice,” she added.