"Stay tuned!" Mr. Trump ended his tweet on the subject.
Writing on Twitter he said: "The Fake News Awards, those going to the most corrupt & biased of the Mainstream Media, will be presented to the losers on Wednesday, January 17th, rather than this coming Monday".
The late-night comedians responded by copying each other in an attempt to get the "Fake News Media" award, expressing the view that receiving an award would be a badge of honor.
Trump latest tweet comes amid a firestorm over an explosive new book about the Trump presidency, "Fire and Fury: Inside the Trump White House". Trump's media dishonesty awards will probably be a blip, but he'll undoubtedly enjoy every minute of coverage they generate.
"TIME "MISTAKENLY" reported that President Trump removed a bust of Martin Luther King, Jr. from the Oval Office", the Trump Campaign said, asking the participants to "let the President know if there is another story you think should be crowned as the 2017 KING of Fake News".
Mr Trump hit back on Twitter, writing: "I think [I] would qualify as not smart, but genius.and a very stable genius at that!"
Another "endorsement" came from Breitbart News, which in July 2016 called the show "political propaganda disguised as entertainment".
Directing his words to Trump, he added: "Personally, I'm excited for your Dishonest & Corrupt Media Awards".
He has quite often described these popular media houses as "fake" media.
It is unclear how Mr Trump's awards will be judged.