In an interview with Anderson Cooper that aired Monday on CNN, the beleaguered Los Angeles Clippers owner said Johnson was the reason he did not apologize sooner for the recorded remarks that got him banned for life from the NBA.
Sterling told Cooper that Johnson telephoned him after the tape was released to the media and that Johnson told him not to make any public response.
"He said, 'Don't do anything.' He said, 'Wait, be patient, I'll help you,'" Sterling said.
"I think he wanted me to just do nothing so he could buy the team," Sterling said.
Johnson, who is scheduled to appear on Cooper's show to reply on Tuesday, wrote on his Twitter account that "I'd rather be talking about these great NBA Playoffs than Donald Sterling's interview." Johnson later Tweeted, "After this week, no more Sterling talk."
NBA Commissioner Adam Silver responded to Sterling's comments on Monday night.
"While Magic Johnson doesn't need me to, I feel compelled on behalf of the NBA family to apologize to him that he continues to be dragged into this situation and be degraded in such a malicious and personal attack," Silver said in a statement.
He added, "The NBA Board of Governors is continuing with its process to remove Mr. Sterling as expeditious as possible."
Sterling, 80, singled out Johnson when he told V. Stiviano in their recorded conversation not to bring blacks to Clippers games.
In the interview, which aired Monday, Sterling said Stiviano had told him she was going to bring some "beautiful black men" to the games and he was "a little jealous" because he wanted the woman -- who is three decades his junior - for himself.
Sterling's rant prompted Silver to ban him for life from the NBA and slap him with a $2.5 million fine. Silver has also urged NBA owners to force Sterling to sell the Clippers.
Repeatedly insisting that he is not a racist, Sterling said he was "baited" into making the remarks and then launched into an attack on Johnson.
"He acts so holy. I mean, he made love to every girl in every city in America," Sterling said.
"What has he done? Can you tell me? Big Magic Johnson - what has he done? He's got AIDS."
Cooper pointed out that Johnson has been diagnosed with HIV but does not have AIDS.
Sterling continued to criticize Johnson's character and insisted that the former Los Angeles Lakers star is not a good role model.
"What kind of a guy goes to every city and sex with ever girl and then he catches HIV?" Sterling said. "Is that someone we want to respect and tell our kids about?
"I think he should be ashamed of himself," Sterling said. "I think he should go into the background."
Sterling also contended that Johnson, founder of the Magic Johnson Foundation, does not do anything for the African-American community.
"What does he do for the black people? He doesn't do anything," Sterling said.
The Magic Johnson Foundation works to promote HIV/AIDs awareness and develop programs and support community-based organizations that address educational, health and social needs in ethnically diverse, urban communities.