The exchange marked a new low for Trump's relationship with journalists, which has largely been hostile.
President Trump faced a very antagonistic media on the day after the midterm elections, offering a soft tone about his desire to work across the aisle with Nancy Pelosi and Democrats in the House.
Trump's Republican party managed to keep its majority in the Senate but lost control of the House of Representatives.
Trump added that the way Acosta had treated Press Secretary Sarah Sanders was "awful".
Acosta questioned him about his rhetoric on immigration during the campaign and his deployment of troops to the USA border with Mexico purportedly to stop a so-called "caravan" of migrants.
The President then said "that's enough" before pointing at another reporter to ask a different question.
Earlier in the day Trump called Acosta "a rude, bad person" as he tried to ask the president a question. "I tell you what, CNN should be ashamed of itself having you working for them". Go ahead. You are a very rude person, the way that you treat Sarah Huckabee Sanders is frightful. "And the way you treat other people is frightful". "You shouldn't treat people that way".
To PBS NewsHour's Yamiche Alcindor, who asked him about white nationalists emboldened by Trump labeling himself a "nationalist", Trump said he was insulted.
The White House has suspended the press access of CNN reporter Jim Acosta after a fiery exchange during a press conference today.
"As a result of today's incident, the White House is suspending the hard pass of the reporter involved until further notice". I didn't call you.'10. She dodged the question, only answering with, "I think the president has made his position known". You are a rude, awful person. After delivering prepared remarks, he fielded questions from reporters for almost 90 minutes on Wednesday, asserting the results marked a win for the GOP, defending his impact, and expressing eagerness to work on bipartisan legislation with House Democrats.
Sarcastically thanking him, Trump bluntly dismissed his comments and denied an ad campaign featuring migrants climbing a wall were "Hollywood actors".