TRUMP: I'll tell you what, CNN should be ashamed of itself having you working for them.
"She has the residue of hate, you know", Ryan said about her fellow reporter.
Acosta began by asking Trump about the migrant caravan that is now making its way to the United States-Mexico border from Central America. He added that the president did not want to be faced with his "lie" about the caravan being an invasion.
"Thank you for telling me that, I appreciate that", Trump responded dryly. Trump told Acosta to let him do his job.
Acosta then pointed out the caravan is hundreds of miles away.
Trump then turned his attention to NBC's Peter Alexander - who immediately jumped to Acosta's defense.
"God plays a very big role in my life", Trump said. "Why doesn't CNN and all journalists who check and verify everything they report sue trump for slander?"
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Trump's ongoing feud with CNN has seen the president skip over Acosta at press conferences, and has seen the president's supporters boo the reporter at rallies.
Some Democrats in the House of Representatives, where the party now has a majority, have threatened to use the subpoena power they will gain in January to investigate Mr Trump and his administration's actions.
To PBS NewsHour's Yamiche Alcindor, who asked him about white nationalists emboldened by Mr Trump labelling himself a "nationalist", Mr Trump said he was insulted.
Acosta again tried to badger Trump, and the president lost his cool, shouting "that's enough!" at the reporter. The way you treat Sarah Huckabee is frightful, and the way you treat other people are awful.
He also said that "I retired" Jeff Flake, the Senate Republican from Arizona who has criticized him. "You aren't the best".
Trump said at a post-election news conference that Democrats and Republicans should set aside partisanship to work together for the American people.
"On the campaign trail you called yourself a nationalist", she asked. "You shouldn't be working for CNN.the way you treat other people is terrible".
"He made it worse" by calling the question racist, Bash said. The freedom of the press is protected by the Constitution.