Six-time major champion Phil Mickelson "sincerely regrets" his criticism of Saudi Arabia's regime and will take a break from the game "to work on becoming the man I want to be".
However the 51-year-old says his comments were "reckless" and he is "deeply sorry for his choice of words".
"I'm beyond disappointed," he said.
Comments made in November to writer Alan Shipnuck, who has authored a soon-to-be-published unauthorised biography of the US PGA champion, were made public by the writer last Friday.
Following their publication, big-name American players Bryson DeChambeau and Dustin Johnson distanced themselves from the proposed league, which is to be a lucrative Formula One-style tour funded by Saudi Arabia's Public Investment Fund.
Both players were expected to be leading figures in the breakaway set-up.
It is thought Mickelson's remarks, in which he branded the Saudi regime as "scary" and that the project was a "once in a lifetime opportunity to reshape how the PGA Tour operates", prompted DeChambeau and Johnson to side with the status quo.
In a statement issued by his management company SportFive, Mickelson said: "Although it doesn't look this way now given my recent comments, my actions throughout this process have always been with the best interest of golf, my peers, sponsors, and fans.
"There is the problem of off-record comments being shared out of context and without my consent, but the bigger issue is that I used words I sincerely regret that do not reflect my true feelings or intentions.
"It was reckless, I offended people, and I am deeply sorry for my choice of words. I'm beyond disappointed and will make every effort to self-reflect and learn from this."
The left-hander, one of the greatest players in the history of the game, says he is suffering mentally from a long career in the spotlight.
"I have made a lot of mistakes in my life and many have been shared with the public," he said in his statement.
"The past 10 years I have felt the pressure and stress slowly affecting me at a deeper level.
"I know I have not been my best and desperately need some time away to prioritise the ones I love most and work on being the man I want to be."
However Mickelson reiterated his belief that professional golf needs to be shaken up and says he has worked closely with the Greg Norman-fronted LIV Golf Investments, who are behind plans for the super league.
"Golf desperately needs change," he said. "And real change is always preceded by disruption. I have always known that criticism would come with exploring anything new.
"I still chose to put myself at the forefront of this to inspire change, taking the hits publicly to do the work behind the scenes.
"My experience with LIV Golf Investments has been very positive. I apologise for anything I said that was taken out of context.
"The specific people I have worked with are visionaries and have only been supportive."
Mickelson has given his long-term sponsors "the option to pause or end the relationship as I understand it might be necessary given the current circumstances".
The veteran, who became the oldest man to win a major when he claimed the US PGA at Kiawah Island last May, received heavy criticism for the comments published last week.
Rory McIlroy branded them "naive, selfish, egotistical and ignorant".