The pledge came in a statement signed by the same four administrators who threatened the possibility of disqualification or suspension for Osaka on Sunday if she continued to skip news conferences.
The four-time major champion and No. 2-ranked player was fined $15,000 when she didn't speak to reporters after her first-round victory at Roland Garros on Sunday. The next day, Osaka pulled out of the tournament entirely, saying on social media that she experiences "huge waves of anxiety" before meeting with the media and revealing she has "suffered long bouts of depression."
Osaka, a 23-year-old who was born in Japan and moved with her family to the U.S. at age 3, said she would "take some time away from the court now, but when the time is right I really want to work with the Tour to discuss ways we can make things better for the players, press and fans."
Tennis players are required to attend news conferences if requested to do so; Grand Slam rules allow for fines up to $20,000 if they don't show up.
"On behalf of the Grand Slams, we wish to offer Naomi Osaka our support and assistance in any way possible as she takes time away from the court. She is an exceptional athlete and we look forward to her return as soon as she deems appropriate," Tuesday's statement from those in charge of the French Open, Wimbledon, US Open and Australian Open said. "Mental health is a very challenging issue, which deserves our utmost attention. It is both complex and personal, as what affects one individual does not necessarily affect another. We commend Naomi for sharing in her own words the pressures and anxieties she is feeling and we empathize with the unique pressures tennis players may face."
French tennis federation president Gilles Moretton, All England Club chairman Ian Hewitt, U.S. Tennis Association president Mike McNulty and Tennis Australia president Jayne Hrdlicka pledged to work with players, the tours and media "to improve the player experience at our tournaments" while making sure the athletes all are on a "fair playing field, regardless of ranking or status."
In a separate statement issued Tuesday to the AP via email, International Tennis Federation official Heather Bowler said the sport will "review what needs to evolve" after Osaka "shone a light on mental health issues."
"It's in all our interests to ensure that we continue to provide a respectful and qualitative environment that enables all stakeholders to do their job to their best ability, without impacting their health, and for the good of the sport," Bowler wrote.
Various players, including Serena Williams, offered support for Osaka and praised her for being forthcoming in her statement on social media Monday.
"It's hard. Nobody really knows what anyone is going through, no matter how much they choose to show on the outside. I had no idea about her. But I respect her openness," 20-year-old American Ann Li said after winning her first-round match Tuesday at Roland Garros. "Our generation is becoming more open and open, which can be a good thing and also a bad thing sometimes. I hope she's doing OK."
On Tuesday, when asked how she handled media attention and duties during her career, Venus Williams said each person is different.
"For me, personally, how I deal with it was that I know every single person asking me a question can't play as well as I can and never will, so no matter what you say or what you write, you'll never light a candle to me," Williams said. "So that's how I deal with it. But each person deals with it differently."
Gael Monfils, 34, who also won Tuesday in Paris, said he could relate to Osaka's concerns to an extent.
"It's a very tough situation for her. I feel for her, because I have been struggling quite a lot as well," said Monfils, of France. "What she's dealing is even tough for me to even judge, because I think she has massive pressure from many things. I think she's quite young. She's handling it quite well. Sometime we want maybe too much from her ... so sometime, for sure, she is going to do some mistake."
And then Monfils offered a sentiment surely shared by many around tennis, from tournament and tour officials to athletes to the sport's fans.
"We need Naomi. We need her definitely to be 100 percent," Monfils said. "We need her back on the court, back [at] the press conference -- and back happy."
The Women's Tennis Association told ESPN it could not comment on a specific player but stated that it "has provided staff dedicated to the mental health of WTA athletes for more than 20 years," including a mental health care provider, in person, at tournaments, and telehealth sessions between tournaments upon request.
The WTA said it also provides resources and support across four primary areas of need, including "1) Mental Health Consultation, Support and Referrals; 2) Mental Performance Skills; 3) Tour Life Skills Development and Strategies; and 4) Critical Incident Management/Safeguarding Support."
Information from The Associated Press was used in this report.