WRU Group Chief Executive Roger Lewis said: "We have carefully considered with Gareth Thomas the decision of the Disciplinary Committee and have also consulted with our lawyers. We have paid particular attention to the reasons given by the Committee by way of justification of a sentence which we regard as severe.
"Whilst we think there are grounds for challenging the sentence neither Gareth nor the Welsh Rugby Union consider it would be in his best interests, or the best interests of the game, for an appeal to be lodged."
Gareth Thomas said: "I would like to thank my teammates, coaches and the Welsh Rugby Union for the support I have been given during this very difficult time. Now I just want to resume training and support the Wales team to a victory over Ireland in Cardiff on Sunday. I will be with them heart and soul just like every other Welsh fan. I will be standing shoulder to shoulder with the team throughout the RBS Six Nations."
At the disciplinary hearing messages of support for the player had been given by former Wales Coach and current All Blacks Assistant Coach Steve Hansen, the 2005 British & Irish Lions Manager Bill Beaumont and the former England and British & Irish Lions player Matt Dawson.