Mr. Lemon, who previously hosted a 10 p.m. show, has lamented CNN’s declining prime-time ratings to some colleagues, according to two people who requested anonymity to share private conversations.

Hours before the dueling statements, Mr. Lemon, 57, appeared on air in his usual anchor chair on “CNN This Morning,” the show he had hosted since November with Poppy Harlow and Kaitlan Collins.

Mr Musk also hit out at Mr Lemon in a post on X on Wednesday, saying that “his approach was basically just ‘CNN, but on social media’, which doesn’t work, as evidenced by the fact that CNN ...