Last November, the United States Golf Association and the Royal and Ancient (R&A) said they wanted to enforce the ban starting in 2016, but US Tour Commissioner Tim Finchem came out against that plan last Sunday.
Since Finchem's comments, two of the leading names in the game, world number one Rory McIlroy and now Woods, have come out in favour of supporting the governing bodies.
Finchem's stance has raised fears of different regulations being in effect for the European Tour and the US Tour in the United States and Woods is among those concerned.
"My position hasn't changed. I still think it should be swung, it shouldn't be anchored and that hasn't changed at all," Woods said, after the Pro-Am ahead of the Honda Classic.
"Obviously nothing is set in stone, nothing is firm. The USGA and the R&A are the governing bodies of our rules and we will see what happens.
"Hopefully we don't have to bifurcate or adapt a local rule like we do sometimes out here on tour with stones and bunkers and things like that. Hopefully we won't have to do that with the putter."
Three of the last five Major tournaments have been won by players using long, or belly, putters - Keegan Bradley at the PGA Championship, Ernie Els at The Open and Webb Simpson at the US Open.
With those three players all being full-time members of the US Tour, Woods said he understood Finchem's stance but said it would not make him chance his view.
"I understand that. I get it. All three of them play our tour full-time, have won Major championships with an anchored putter. I understand his position but I still feel that all 14 clubs should be swung. That hasn't changed nor will it ever," said the 14-times Major winner.
On Tuesday McIlroy urged the US Tour to fall in line with whatever decision is made by the two governing bodies.
"We've trusted this game of golf; we've put it in the hands of the R&A and the USGA for I don't know how many years, and we've always abided by the rules that they have set," McIlroy said.
"I don't think this should be any different. I think golf is pretty good at the minute and it's in good hands."
But South African Els, who has used a long putter for the past year, praised Finchem for taking a stand.
"You've got to give the commissioner credit, supporting his players and going against what the governing bodies want to do or might be doing," he told reporters.
"He came out and made his position very clear where the tour stands on that issue and obviously you're going to have different kind of reactions around the world, but at least the rest of the world knows where he's coming from and where what the tour stance is, and that was important to do."
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