At the end of last month, the PGA Tour came out against the ban, joining the PGA of America in opposing the move.
But the European Tour has backed the proposals put forward by the game's governing bodies, the R&A and USGA, although support from the tournament committee and player representatives was not unanimous.
A statement from the European Tour read: "The European Tour has confirmed its support for the R&A and the USGA and their proposal for rule 14-1b - the prohibition of anchoring any club when making a stroke under the Rules of Golf."
Chief executive George O'Grady added: "The European Tour has been fully involved in the consultation process which ended on February 28, and deeply value this involvement. Our members support the unique role played by the governing bodies in formulating the Rules of Golf.
"Additionally, virtually all of our tournament committee and player representatives support the proposed rule even though they are aware, and have taken into account, the fact that some members and especially our senior members use the anchored method.
"We understand the points put forward by the PGA Tour and the PGA of America and respect and sympathise with their views, which are based on their experience and the evidence before them, and have been expressed with great concern for the game.
"The whole issue has received far greater focus and comment in the United States than in the rest of the world, perhaps because of the numbers of their golfers using the anchored method, and the set up in general terms of their golf courses and the firmness and speed of their greens."
When announcing the PGA Tour's stance, commissioner Tim Finchem said there was an "absence of data or any basis to conclude that there is a competitive advantage to be gained by using anchoring", suggesting there was no need for a ban.
And although he did not specify what would happen if the ban comes into force, there is a real danger of different rules being applied at different events.
The PGA Tour runs the lucrative American circuit and plays a dominant role in staging World Golf Championship events.
Traditionally they adopt the rules of golf as determined by the R&A and USGA, who run the Open Championship and US Open respectively, while the PGA of America organise the US PGA Championship and American Ryder Cup team.