The media outlet reported among the comments, Robinson described himself as a "black Nazi" and described how he used to go "peeping" on women at a public gym when he was 14 and expressing support for reinstating slavery on a pornographic website Nude Africa.
Several of his campaign staffers resigned after the report came out.
From the beginning, the lieutenant governor denied these alleged comments, calling the report lies. In his lawsuit, Robinson is seeking $50 million in damages from CNN.
His lawyers say the news conference Tuesday morning focused on -- what they call -- CNN's "salacious, coordinated, and disgraceful smear campaign and election interference" against Robinson.
Robinson had made it clear he was not dropping out of the race for state governor. Previously, he said his team is working to fill those roles as he continues his campaign.
Election Day is just three weeks away.
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Mark Robinson vows to stay in the race, calls reports of his porn message board use 'tabloid trash'