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With Trump looking to call on other reporters, CNN journalist Jim Acosta yelled out, "Since you are attacking us, can you give us a question?"
"Not you," Trump said, adding that, "Your organisation is terrible!"
The reporter pressed on saying, "You are attacking our news organisation, can you give us a chance to ask a question, sir?" Trump countered by telling him "don't be rude".
"I'm not going to give you a question," Trump responded.
"I'm not going to give you a question. You are fake news!" the President-elect asserted.
Trump dismissed as "nonsense" the media claims that Russia has compromising information on him, saying the allegations may have been leaked by US intelligence agencies and it would be a "tremendous blot" on their record if they did that.
"It's frankly outrageous and highly irresponsible for a left-wing blog...To drop highly salacious and flat-out false information on the Internet just days before he takes the oath of office," he said, referring to BuzzFeed.
"The fact that BuzzFeed and CNN made the decision to run with this unsubstantiated claim is a sad and pathetic attempt to get clicks," he said during the press conference.