Apologised to Naomi after controversial US Open defeat: Serena  

Tennis star Serena Williams has revealed that she has apologised to Japan's Naomi Osaka who defeated her in the finals of the US Open last year.

Naomi had defeated Serena 6-2, 6-4 in New York to win her first major in September last year. However, it was overshadowed by controversy, with the American tennis star clashing with chair umpire Carlos Ramos, culminating when he docked her a game for calling him a "thief."

However, in an essay published on Tuesday in Harper's Bazaar, a link to which was put on Instagram by Serena, the 37-year-old said she had apologised to Naomi for the "debacle" that "ruined something that should have been amazing and historic."

"Not only was a game taken from me but a defining, triumphant moment was taken from another player, something she should remember as one of the happiest memories in her long and successful career," the 37-year-old Williams wrote. "My heart broke."

As the days passed, the 23-time Grand Slam champion said she started seeing a therapist and wasn't ready to pick up a tennis racket. She decided to write to Osaka, and here is what she said:

"Hey, Naomi! It's Serena Williams. As I said on the court, I am so proud of you and I am truly sorry. I thought I was doing the right thing in sticking up for myself. But I had no idea the media would pit us against each other. I would love the chance to live that moment over again. I am, was, and will always be happy for you and supportive of you. I would never, ever want the light to shine away from another female, specifically another black female athlete. I can't wait for your future, and believe me I will always be watching as a big fan! I wish you only success today and in the future. Once again, I am so proud of you. All my love and your fan, Serena."

In the essay, Serena also included Naomi's response which she said made her cry.

"People can misunderstand anger for strength because they can't differentiate between the two," Naomi said, according to Serena. "No one has stood up for themselves the way you have and you need to continue trailblazing."

The 37-year-old went on to write in the essay: "It was in this moment that I realized the real reason the US Open was so hard for me to get over: It wasn't because of the backlash I faced but rather because of what had happened to the young woman who deserved so much more in her special moment. I had felt that it was my fault and that I should have kept my mouth closed. But now, seeing her text putting everything in perspective, I realized she was right."

"Ultimately, my daughter is the reason I use my voice, the reason I picked up a racket again," she added.

Meanwhile, Serena had advanced to the semifinals of the ongoing Wimbledon after she defeated American compatriot Alison Riske on Tuesday.