Phil Mickelson has expressed his “deepest sympathy” to the families of those who lost loved ones in the 9/11 terrorist attacks in the wake of stinging criticism of his decision to join the Saudi-backed LIV Golf Series.

A group representing victims’ families and survivors accused Mickelson and a number of fellow high-profile American players of sportswashing and betraying their country by competing in last week’s event at Centurion Club.

Asked about the letter written by Terry Strada, the national chair of 911familiesunited.org, in a press conference ahead of the US Open, a visibly uncomfortable Mickelson said: “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 emphasise that enough. I have the deepest of sympathy and empathy for them.”

Pressed on whether he would respond privately to the letter, Mickelson largely repeated his earlier answer and his comments cut little ice with Strada, a mother of three whose husband Tom died in the attack on the north tower of the World Trade Centre.

She told the PA news agency: “Phil knows exactly what he’s doing, and he and his fellow LIV golfers should be ashamed.

“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 (Jay Monahan) said Sunday, ‘You’d have to be living under a rock’ to not understand the implications of involving yourself with the Saudis.”

Mickelson and the other 16 PGA Tour members who competed in the first LIV Golf event without permission were instantly suspended by the Tour, although some had already resigned their membership.

That is something Mickelson has no intention of doing and he would still like to play on the PGA Tour in the future, even though he has already won four times on the Champions Tour.

“My preference is to be able to choose which path I would like, one or the other or both,” said Mickelson, who will celebrate his 52nd birthday on Thursday.

“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.”

Mickelson was as cagey with his answers as he was at Centurion, but did concede that the “incredible financial commitment” – which he tacitly confirmed last week was 200million US dollars (£159.5m) – “allows me to have more balance in my life”.

Victory on Sunday would see Mickelson become the sixth player to complete a career grand slam, although he admits that will be difficult given his lack of competitive golf.

“That’s going to be a challenge, right. It’s the most difficult test in golf,” said Mickelson, who shot 10 over par to finish in a tie for 33rd last week in his first event since February.

“I think it was important for me to have a little bit of competitive golf last week and identify some of the areas of weakness. It was one of the worst putting tournaments I’ve had in years.

“I spent time (on Sunday) addressing that, which is why I basically putted the whole day on the course. In the off-season I actually made some strides ball-striking-wise, and I’m fairly optimistic there, but it will be a real challenge.

“These are the best players in the world, and it’s the hardest test of the year. It looks that it’s going to be a brutal test of golf, and that’s what this championship is all about.”