The PGA Tour has suspended members who have competed in the Saudi-funded breakaway without permission, while the DP World Tour fined players £100,000 and banned them from the Genesis Scottish Open, but saw that temporarily stayed on appeal.
R&A chief executive Martin Slumbers said in July that banning LIV players from next year's Open was "not on the agenda", but did not rule out changing the championship's entry criteria.
Masters chairman Fred Ridley took a similar stance on Tuesday, saying in a statement that the entry criteria for 2023 would remain the same, with any possible future changes announced in April.
Former Masters champions Phil Mickelson, Dustin Johnson, Sergio Garcia and Bubba Watson are among the top players to have joined LIV, while others who remain inside the world's top 50 - despite LIV not currently being allowed to award ranking points - will still be eligible to compete at Augusta National.
Ridley's statement read: "From its inception in 1934, the purpose of the Masters Tournament has been to benefit the game of golf.
"Each April, the Masters assembles the world's leading golfers to compete for the Green Jacket and a place in history.
"It provides a stage for fans to experience dramatic moments of competition at the highest level and promotes the sport domestically and abroad.
"Through the years, legends of the game have competed and won at Augusta National Golf Club.
"Champions like Gene Sarazen, Byron Nelson, Ben Hogan, Sam Snead, Arnold Palmer, Gary Player, Tom Watson, Jack Nicklaus and Tiger Woods have become heroes to golfers of all ages.
"They have inspired some to follow in their footsteps and so many others to play and enjoy the game. They have supported the sport and, thus, all who benefit from it.
"They have shown respect for those who came before them and blazed a trail for future generations. Golf is better because of them.
"Regrettably, recent actions have divided men's professional golf by diminishing the virtues of the game and the meaningful legacies of those who built it.
"Although we are disappointed in these developments, our focus is to honour the tradition of bringing together a preeminent field of golfers this coming April.
"Therefore, as invitations are sent this week, we will invite those eligible under our current criteria to compete in the 2023 Masters Tournament.
"As we have said in the past, we look at every aspect of the Tournament each year, and any modifications or changes to invitation criteria for future Tournaments will be announced in April.
"We have reached a seminal point in the history of our sport. At Augusta National, we have faith that golf, which has overcome many challenges through the years, will endure again."