By Ben Morse, CNN

Phil Mickelson says he has "deep empathy" for the victims of the 9/11 terror attacks following criticism of the 51-year-old and other US golfers for joining the controversial Saudi-backed LIV Golf series.

The six-time major winner featured in the inaugural event of the new venture last week at the Centurion Club near London.

The letter sent by 9/11 Families United -- a coalition of families and survivors of the 2001 terror attacks -- to Mickelson, Dustin Johnson, Bryson DeChambeau, Patrick Reed and Kevin Na, expressed their "outrage" at the players participating in "the multi-billion dollar 'sports washing' campaign."

On Monday, in an uncomfortable press conference for Mickelson, the six-time major winner was questioned by reporters on the letter -- written by the group's chair Terry Strada -- ahead of the beginning of the US Open on Thursday.

"I would say to the Strada family, I would say to everyone that has lost loved ones, lost friends on 9/11 that I have deep, deep empathy for them. I can't emphasize that enough," Mickelson said.

"I have the deepest of sympathy and empathy for them."

When he was asked later in his press conference whether he would privately respond to Strada's letter, Mickelson repeated the sentiment of his earlier answer.

"I think I speak for pretty much every American in that we feel the deepest of sympathy and the deepest of empathy for those that have lost loved ones, friends in 9/11. It affected all of us, and those that have been directly affected I think -- I can't emphasize enough how much empathy I have for them."

Later on Monday, Strada released a statement in response to Mickelson's answers.

"Phil knows exactly what he's doing, and he and his fellow LIV golfers should be ashamed," wrote Strada, whose husband Tom died in the World Trade Center's North Tower.

"They are helping the Saudi regime 'sportswash' their reputation in return for tens of millions of dollars, at the very same time our government is rolling out more damning evidence of Saudi culpability in the 9/11 attacks.

"As the PGA Tour commissioner said Sunday 'you'd have to be living under a rock' to not understand the implications of involving yourself with the Saudis."

CNN has contacted LIV Golf for comment and has yet to receive a response.

Following an executive order by President Joe Biden in 2021 to declassify 9/11 documents, the Federal Bureau of Investigation made public documents related to its investigation of the 9/11 terrorist attacks and suspected Saudi government support for the hijackers.

The first of which, released last year and which is from 2016, provides details of the FBI's work to investigate the alleged logistical support that a Saudi consular official and a suspected Saudi intelligence agent in Los Angeles provided to at least two of the men who hijacked planes on September 11, 2001. The document, released on the 20th anniversary of the deadly attacks, still contains significant redactions.

It details multiple connections and witness testimony that prompted FBI suspicion of Omar al-Bayoumi, who was purportedly a Saudi student in Los Angeles but whom the FBI suspected to be a Saudi intelligence agent. The FBI document describes him as deeply involved in providing "travel assistance, lodging and financing" to help the two hijackers.

Fifteen of the 19 al Qaeda terrorists who hijacked four planes on September 11, 2001, were Saudi nationals.

In September 2021, 9/11 Families United said the report "puts to bed any doubts about Saudi complicity in the attacks."

The Saudi government has repeatedly denied any government involvement in the attacks. On Tuesday, CNN contacted Saudi Arabia for comment and has yet to receive a response.

Mickelson was one of 17 players suspended by the PGA Tour for participating in the new big-money LIV Golf league.

The LIV Golf series, which is backed by Saudi Arabia's Public Investment Fund (PIF), has threatened to unsettle golf's traditional set up by providing eye-watering sums of money for players to earn away from the established golf tours.

But Mickelson and the other breakaway players have faced criticism for their decision to leave the PGA Tour and the DP World Tour.

It has led to some uncomfortable press conferences for Mickelson, where he has repeatedly faced tough questions on the subject of leaving the PGA Tour and the human rights record of Saudi Arabia.

However, he says he "respects" if people disagree, but in his opinion, moving to the LIV Golf series "at this time this was the right decision" for him.

Going forward, Mickelson says he hopes golfers can have a choice in where they ply their trade and not be restricted.

"My preference is to be able to choose which path I would like, one or the other or both," he explained.

"I feel that... I gave as much back to the PGA Tour and the game of golf that I could throughout my 30 years here, and through my accomplishments on the course, I've earned a lifetime membership. I intend to keep that and then choose going forward which events to play and not."

The 2022 US Open begins on Thursday at Brookline in Massachusetts, with Mickelson among those taking to the course.

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