"I'm not a racist," Sterling told CNN's Anderson Cooper in excerpts posted from an interview taped Sunday and set to air Monday. "I made a terrible mistake. I'm here to apologize."
In his first public comments since being banned for life from the NBA, Sterling said years of good behavior as an owner should count toward his future.
"I'm a good member who made a mistake," Sterling said. "Am I entitled to one mistake, am I after 35 years? I mean, I love my league, I love my partners. Am I entitled to one mistake? It's a terrible mistake, and I'll never do it again."
The interview came nearly two weeks after NBA Commissioner Adam Silver banned Sterling, fined him $2.5 million and urged the other league owners to force him to sell the team.
Sterling said he waited to make a public apology because he was "emotionally distraught."
"The reason it's hard for me, very hard for me, is that I'm wrong," Sterling said. "I caused the problem. I don't know how to correct it."
He later added, "If the owners feel I have another chance, then they'll give it to me."
Sterling's comments came on the same day ABC News posted excerpts of an interview his estranged wife gave to Barbara Walters.
Shelly Sterling said she would fight to keep her 50 percent ownership stake of the team.
"I will fight that decision," Shelly Sterling said. "To be honest with you, I'm wondering if a wife of one of the owners, and there's 30 owners, did something like that, said those racial slurs, would they oust the husband? Or would they leave the husband in?
"I don't know why I should be punished for what his actions were."
NBA spokesman Mike Bass released a statement Sunday night in response to Shelly Sterling's comments.
"Under the NBA constitution, if a controlling owner's interest is terminated by a three-quarter vote, all other team owners' interests are automatically terminated as well," Bass said. "It doesn't matter whether the owners are related as is the case here. These are the rules to which all NBA owners agreed to as a condition of owning their team."
Shelly Sterling's attorney, Pierce O'Donnell, responded to the NBA's statement.
"We do not agree with the league's self-serving interpretation of its constitution, its application to Shelly Sterling or its validity under these unique circumstances," O'Donnell said. "We live in a nation of laws. California law and the United States Constitution trump any such interpretation."
ABC posted initial excerpts of Shelly Sterling's interview and planned to air the rest of it Monday.
Shelly Sterling also said she "eventually" will divorce her husband, and that she hadn't yet done so due to financial considerations.
"For the last 20 years, I've been seeing attorneys for a divorce," she said. "In fact, I have here - I just filed - I was going to file the petition. I signed the petition for a divorce. And it came to almost being filed. And then, my financial adviser and my attorney said to me, 'Not now.'"
LeBron James said Sunday after the Miami Heat practiced for Game 4 of the Eastern Conference semifinals against the Brooklyn Nets that NBA players believe nobody in the Sterling family should be able to own the Clippers if he's gone.
"As players, we want what's right and we don't feel like no one in his family should be able to own the team," James said.