An arbitration panel this month ruled that the DP World Tour was correct to impose sanctions on members who appeared on the rebel LIV circuit without permission.
It came after England's Ian Poulter and Lee Westwood were among 12 players appealing against punishments the tour wanted to impose on those who took part in the inaugural LIV event near London last year.
It remains to be seen whether they will appeal or give up their membership of the DP World Tour -- a move that would end their involvement in the Ryder Cup.
Norman would not comment on ongoing legal matters, but said: "All I can tell you is this: From a LIV perspective, we'll always support our players.
"We always have said that since day one," he said in Adelaide ahead of LIV's inaugural tournament in Australia.
"We believe in where we're going and we're going to be unwavering in that commitment."
The launch of the Saudi-backed LIV Golf last year divided the sport, with big-name players lured by huge contracts defecting from the PGA Tour and DP World Tour.
Acrimony and legal battles with US and European golf powerbrokers continue to mar the game.
But Norman also offered an olive branch, reiterating that he was keen to sit down for talks with both the DP World Tour and PGA Tour.
"LIV is not changing anything and we've always been consistent for the last 15 months of saying we're happy to sit down with you, we're happy to talk to you," the Australian said.
"We did with the DP World Tour. We've tried with the PGA Tour, consistently with zero, zilch, nothing. That's their choice. If that's your decision, fine, we're okay with that.
"But I do hope there gets to a position where there is a resolution to this because the game of golf doesn't need to suffer. These guys (players) don't need to suffer."
WOMEN'S TOUR
Norman is also considering creating a women's circuit and has approached American and European players who are keen to be involved.
"That is a discussion we have internally on a regular basis. I have personally had discussions with individual LPGA Tour players, LET Tour players, Ladies European Tour. They love what our product is showcasing," he claimed.
"They ask all the time, 'How can we get involved?' We'd love to see a LIV ladies series."
But Norman is also conscious that he first needs to get the men's version right, with the tour still finding its feet in only its second season.
"From our perspective, last year was a beta season. We had eight events. This year was our first season where we're kicking off," he said.
"We can only drink out of a fire hydrant so much, so we have a lot of opportunities and initiatives coming across our plate.
"Our focus is to make sure this year we produce what we're producing here from day one, 2023, and then going forward we're looking what are the best opportunities to build on to what we have today.
"But the answer to the question is yes, we talk about it (women's version) internally, and I have had discussions with individual lady players, professional players."
