"Simone will continue to be evaluated daily to determine whether or not to participate in next week's individual event finals.
"We wholeheartedly support Simone's decision and applaud her bravery in prioritising her well-being. Her courage shows, yet again, why she is a role model for so money."
The decision marks a stunning turn of events for Biles, who had been widely expected to crown the greatest career in gymnastics history with another multiple haul of gold medals in Tokyo.
The diminutive Texan, winner of four gold medals at the 2016 Rio Olympics, was vying for a potential six golds in Japan.
However her campaign unravelled on Tuesday when she suddenly withdrew from the team final after an uncharacteristically shaky display on the opening vault. Biles later said she had pulled out of the final out of concern for her mental well-being.
"I have to focus on my mental health," Biles said. "I didn't want to go out and do something stupid and get hurt... At the end of the day we don't want to be carried out of there on a stretcher."
Biles' decision has been hailed as a game-changing moment for elite sport, helping to dispel enduring stigmas surrounding mental health.
Biles told US Olympic broadcaster NBC television late Tuesday she would assess her readiness to compete on a "day-by-day" basis.
"Physically, I feel good, I'm in shape," she said on NBC television's Today program. "We're going to take it day by day, and we're just gonna see."
As Biles reflected on her shattered Olympic dreams, she drew broad support from athletes, officials and public figures.
"Simone, you've made us so proud. Proud of who you are as a person, teammate and athlete," said Sarah Hirshland, US Olympic and Paralympic Committee chief executive officer.
"We applaud your decision to prioritize your mental wellness over all else and offer you the full support and resources of our Team USA community as you navigate the journey ahead."
Obama support, Phelps concern
Former US first lady Michelle Obama tweeted: "Am I good enough? Yes, I am. The mantra I practice daily. @Simone_Biles, we are proud of you and we are rooting for you."
Two-time Olympic Alpine ski champion Mikaela Shiffrin offered support as well, tweeting: "@Simone_Biles keep whipping out that smile of yours cause it is undeniably golden. Always."
US swimming and Olympic legend Michael Phelps, who in 2018 revealed his own struggles with depression and suicidal thoughts following the 2012 Olympics, said watching Biles struggle on Tuesday "broke my heart."
Phelps told NBC the Olympics could be overwhelming for athletes, and that he had often struggled to find support during his own career.
"The biggest thing is we all need to ask for help sometimes too when we go through those times," Phelps said. "For me, I can say personally it was something very challenging. It was hard for me to ask for help."
Biles's former USA teammate Aly Raisman spoke of her concerns for her friend's wellbeing.
"I know that all of these athletes dream of this moment for their whole entire lives, and so I'm just completely devastated," Raisman told NBC.
"I am obviously so worried and just hoping that Simone is OK."
Raisman and Biles were among the gymnasts abused by former US team doctor Larry Nassar, who was jailed in 2018 for sexual abuse.
"It's just so much pressure, and I've been watching how much pressure has been on her in the months leading up to the Games, and it's just devastating. I feel horrible," Raisman added.