The heated exchange between Naomi Osaka and Megyn Kelly came hours after Osaka debuted her Sports Illustrated Swimsuit issue cover

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Naomi Osaka called out Megyn Kelly after the journalist took a dig at the number of times the tennis player has appeared in magazines since declining to give interviews at the French Open, citing efforts to preserve her mental health.

The two exchanged online jabs on Monday, with Kelly, 50, first responding to a tweet from conservative sports pundit Clay Travis that read: "Since saying she's too introverted to talk to the media after tennis matches, Naomi Osaka has launched a reality show, a Barbie, and now is on the cover of the SI swimsuit issue."

"Let's not forget the cover of (& interview in) Vogue Japan and Time Mag!" Kelly replied.

In a since-deleted tweet to Kelly, Osaka said her covers were shot before she went public about her struggles with social anxiety, which the athlete has previously said made it "stressful" for her to speak with press.

"Seeing as you're a journalist I would've assumed you would take the time to research what the lead times are for magazines, if you did that you would've found out I shot all of my covers last year," Osaka tweeted back, per a screenshot captured by Sporting News. "Instead your first reaction is to hop on here and spew negativity, do better Megan [sic]." 

Kelly followed up in a subsequent tweet, claiming Osaka had blocked her.

"Poor @naomiosaka blocked me while taking a shot at me (guess she's only tough on the courts)," Kelly wrote. "She is apparently arguing that she shot her many covers b/4 publicly claiming she was too socially anxious to deal w/press."

"Truth is she just doesn't like Qs she can't control. Admit it," the former Fox News host added.

Osaka made the decision to entirely withdraw from the French Open in May after picking up a $15,000 fine for not participating in the tournament's media requirements. She opted not to compete in Wimbledon a month later.

In an essay published by Time on July 8, the tennis pro — who previously shared that she's suffered from depression since 2018 — said athletes deserve "the right to take a mental break from media scrutiny on a rare occasion without being subject to strict sanctions."

"I feel uncomfortable being the spokesperson or face of athlete mental health as it's still so new to me and I don't have all the answers," she wrote in part. "I do hope that people can relate and understand it's okay to not be okay, and it's okay to talk about it. There are people who can help, and there is usually light at the end of any tunnel."

Naomi Osaka
Credit: Naomi Osaka/instagram

Want to get the biggest stories from PEOPLE every weekday? Subscribe to our new podcast, PEOPLE Every Day, to get the essential celebrity, entertainment and human interest news stories Monday through Friday. And listen below for more on what Sports Illustrated Swimsuit's Editor-in-Chief MJ Day had to say about the 2021 Swimsuit issue and Megyn Kelly's comments about Naomi Osaka's Sports Illustrated Swimsuit cover.

While Osaka did not address Kelly beyond her deleted tweet on Monday, she did share with fans on Instagram Story that her Sports Illustrated Swimsuit issue cover, which debuted hours before the Twitter exchange, was shot last year.

Alongside behind-the-scenes footage from the photo shoot, she wrote, "We did this in December and it was freezing."

RELATED VIDEO: Grand Slam Leaders Pledge to Address Tennis Players' Mental Health Concerns, Commend Naomi Osaka

Kelly's tweets about Osaka come just weeks after it was announced her podcast, The Megyn Kelly Show, will soon become a daily 2-hour show on SiriusXM.

"My deal with Sirius is, I can talk about whatever I want. I touch third rails for a living, by design. I'm not built that way: to avoid these things," Kelly told PEOPLE in early July. "I want the fight. I enjoy discussion, fierce discussion and debate. I can't imagine giving that up again."