CNN reporter Jim Acosta fired back at incoming White House press secretary Sean Spicer after the two clashed at President-elect Donald TrumpDonald TrumpTrump takes shot at new GOP candidate in Ohio over Cleveland nickname GOP political operatives indicted over illegal campaign contribution from Russian national in 2016 On The Money — Dems dare GOP to vote for shutdown, default MORE's press conference Wednesday. 

Spicer tweeted that Acosta had been "rude" and demanded he apologize to Trump. 

“An unfortunate statement. Sean you know that you threatened to throw me out of that news conference if I asked another question,” Acosta tweeted back.

Trump, during his press conference Wednesday, repeatedly refused to take a question from Acosta.

"Your organization is terrible," Trump told him. 

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The Trump team has hammered CNN for its reporting Tuesday night on an unverified outside dossier, which makes allegations of Trump's entanglements with Russia. CNN did not publish the full document but reported its claims that Trump aides had been in contact with Russian intermediaries and alleged that Russia had collected disparaging information on Trump. CNN reported that a two-page summary of the dossier was included in intelligence agencies' classified report, given to Trump, on Russia's effort to interfere with the outcome of the 2016 presidential election.

"You're attacking us. Can you give us a question?” Acosta asked at the press conference.

"Don't be rude. No, I'm not going to give you a question. You are fake news," Trump responded, before calling on a reporter from Breitbart News.

Wednesday afternoon, Acosta said in an interview on CNN that Spicer had threatened to remove him from the press conference.

“At one point during this news conference, in the interest of full disclosure ... after I asked and I guess demanded that we had a question, Sean Spicer, the incoming press secretary, did say to me if I were to do that again, I was going to be thrown out of this press conference,” Acosta said.

Spicer responded that Acosta’s statement wasn’t true, prompting Acosta to challenge Spicer.

Spicer continued to hit Acosta on Fox News, demanding Acosta apologize for his "rude" behavior.

"[Trump is] going to set the record straight. He’s not going to let dishonest members of the media have factually inaccurate stories about him, his administration or his attempts to make this country better without him responding and responding forcefully," Spicer told Fox News's Tucker Carlson. "A lot of these folks in the media are used to these politicians sitting back and taking it. That's not who Donald trump is. He fights back and he wins."

"The CNN reporter continued to harass Donald Trump, so I told him he was rude and disrespectful," Spicer said.