"This has been an incredible four years," Trump said in brief remarks to staff, supporters and members of his family gathered at Joint Base Andrews outside Washington.

"We've accomplished so much together," he said. "I will always fight for you.

"We will be back in some form."

Trump did not address Biden by name but said he wishs the new administration "great luck and great success."

Trump will be at his Mar-a-Lago resort in Florida when Biden is sworn in at noon (1700 GMT).

He is the first president in more than 150 years to snub the inauguration of his successor.

Trump also decided to leave a letter to his successor Joe Biden before leaving the White House, spokesman Judd Deere told AFP minutes after his departure. 

Trump, who refused to accept his defeat for more than two months, never congratulated Joe Biden on his victory.

"We are just temporary occupants of this office," Barack Obama wrote in his own note to Trump four years ago, left in the Oval Office in line with presidential tradition.

"That makes us guardians of those democratic institutions and traditions... that our forebears fought and bled for. Regardless of the push and pull of daily politics, it's up to us to leave those instruments of our democracy at least as strong as we found them," he added.