President Donald J. Trump. (AP)

(CNSNews.com) -- During a lengthy press conference today, President Donald Trump criticized some news organizations for their apparently hateful and inaccurate coverage, and he jokingly sparred with CNN's Jim Acosta stating that CNN is no longer "fake news" but "very fake news." Trump also lightheartedly asked if CNN's Acosta was in any way related to the new Labor Secretary nominee R. Alexander Acosta.

Jim Acosta said no but added that he liked the title Secretary Acosta. The exchange occurred as follows:

Trump: “Tomorrow they will say, ‘Donald Trump rants and raves at the press.’ I’m not ranting and raving. I’m just telling you – you’re dishonest people. But I’m not ranting and raving. I love this. I’m having a good time doing it."

"But tomorrow the headlines are going to be, ‘Donald Trump rants and raves --.’ I’m not ranting and raving," he said. "Go ahead. Should I let him have a little bit more? What do you think, Peter? Peter, should I let him [Jim] have a little bit more? Sit down [to Peter]. Sit down. We’ll get to you."

CNN’s Jim Acosta: "Just because of the attack of fake news and the attack on our network, I just want to ask you, sir –"

Trump: “I’m changing it from fake news, though – [to] very fake news. Go ahead."

"And you’re not related to our new [Labor Secretary Alex Acosta]? You know, I looked at that name and I said, ‘Wait a minute, is there any relation there? Alex?’ I checked it, they said, ‘No sir.’ I said, ‘Do me a favor, go back and check the family tree.’”