"Being persistent and asking tough questions is his job, and he has our complete support," the network said Monday morning.
Acosta attracted President-elect Donald Trump's ire during a contentious press conference last Wednesday. After Trump criticized CNN from the podium, Acosta interjected and forcefully tried to ask a question.
"I felt it was only fair that if our news organization is going to be attacked, that we get a chance to ask a follow-up question about what Donald Trump was talking about," Acosta said on television afterward.
Incoming White House press secretary Sean Spicer has repeatedly said that Acosta should apologize.
Speaking on Fox News on Sunday, Spicer said, "The idea that he took no responsibility for his behavior was highly unacceptable and inappropriate, and he does owe us and his fellow members of the press corps an apology for his behavior."
Acosta and CNN have declined to apologize.