In the prerecorded message, Trump touted his accomplishments in the White House, saying he and his administration "did what we came here to do -- and so much more," and wished the incoming administration luck.
"This week, we inaugurate a new administration and pray for its success in keeping America safe and prosperous. We extend our best wishes and we also want them to have luck -- a very important word," Trump said, although he did not mention Biden by name throughout the 20-minute address.
As Biden arrived in Washington, D.C., and participated in a ceremony honoring the 400,000 people who have died due to the COVID-19 pandemic, Trump touted the development of vaccines against the virus as a "medical miracle" while mourning the lives lost.
"We grieve for every life lost and we pledge in their memory to wipe out this horrible pandemic once and for all," he said.
Trump also made a brief reference to the Jan. 6 siege on the Capitol building, as his supporters made their way inside as Congress was certifying Biden's election win.
"All Americans were horrified by the assault on our Capitol. Political violence is an attack on everything we cherish as Americans. It can never be tolerated," Trump said.
Last week, Trump became the first president to be impeached twice as the House charged him with inciting the riot in a speech that morning.
He was also banned from multiple leading social media platforms including Facebook, Twitter and YouTube in the aftermath of the riot and in Tuesday's message lamented what he described as "political censorship and blacklisting."
"Shutting down free and open debate violates our core values and most enduring traditions," he said.