The United States Golf Association (USGA) said it was "not appropriate, nor fair to competitors, to change [entry] criteria once established", and that there would be no change to the field for the third men's major of the year.

It means players such as Phil Mickelson - a six-time major champion - and 2016 US Open winner Dustin Johnson will be free to compete at The Country Club in Brookline in Massachusetts.

The American duo are the two most high-profile players to have signed up for the LIV Golf Invitational Series and Johnson quit the PGA Tour in the process, but Mickelson says he has no plans to resign his membership.

Spaniard Sergio Garcia, South African duo Louis Oosthuizen and Charl Schwartzel, Graeme McDowell of Northern Ireland plus Germany's Martin Kaymer are other past major winners to have joined Americans Mickelson and Johnson in the LIV ranks.

Players signing up to play in the LIV Golf Invitational Series have been threatened with exclusion from PGA Tour and DP World Tour events, but golf's majors are organised separately and in the first test case, LIV players are able to compete.

The USGA did insist in a statement that its stance "should not be construed as the USGA supporting an alternative organizing entity, nor supportive of any individual player actions or comments."

"We pride ourselves in being the most open championship in the world and the players who have earned the right to compete in this year’s championship, both via exemption and qualifying, will have the opportunity to do so," the USGA said. 

"Our field criteria were set prior to entries opening earlier this year and it’s not appropriate, nor fair to competitors, to change criteria once established.

"Regarding players who may choose to play in London this week, we simply asked ourselves this question - should a player who had earned his way into the 2022 U.S. Open, via our published field criteria, be pulled out of the field as a result of his decision to play in another event? 

"And we ultimately decided that they should not."

The LIV Golf Invitational Series is particularly controversial because it is majority owned by Saudi Arabia's Public Investment Fund (PIF).

The PIF is Saudi Arabia's sovereign wealth fund and critics say the country is using it for sportswashing.

Mickelson previously admitted the project was "sportswashing", claiming the Saudi partners were "scary motherfuckers to get involved with" and "have a horrible record on human rights", as reported by Fire Pit Collective.

However, he defended the breakaway as being in players' best interests as the PGA Tour is "really a dictatorship".

Homosexuality is illegal in Saudi Arabia, women's rights are severely restricted, as is free speech, and the country is leading a coalition which has carried out deadly airstrikes across Yemen since 2015.

These issues - plus Saudi Arabia's links to the 9/11 terror attacks - have been at the forefront of criticism over certain golfers' willingness to sign up to the breakaway series, which is made up of 54-hole competitions and will see players compete in teams.

The assassination of journalist Jamal Khashoggi by Saudi Government operatives is another bone of contention, but was dismissed by LIV Golf Investments chief executive Greg Norman with the line "we’ve all made mistakes".

Mickelson took a hiatus from golf for several months his comments were published, missing two majors, but plans to return this week at the first LIV event in England.

He is then due to play in the US Open - the only major he is yet to win.

One player who will not take part in the US Open is Tiger Woods.

The American star, a 15-time major winner, will instead focus on July's British Open amid ongoing fitness struggles.

Woods turned down a "mind-blowingly enormous" nine-figure offer to play in LIV events, according to Norman.