"In his desire to be in the limelight it would appear that he [Tutu] has become a friend of the enemy instead of a friend of God.
"It is our opinion that should Jesus Christ have been on the Earth today He would have greeted him with the same disdain that He treated the Pharisees of His day by calling him a ‘hypocrite', 'whited sepulchre' and ‘a son of Satan'," party leader Theunis Botha said in a statement.
He was responding to Tutu's opinion piece on assisted dying, published in the British Observer newspaper on Saturday ahead of a House of Lords debate on the issue to be held on Friday.
"To his support for abortion and same-sex-marriage, Bishop Tutu now adds euthanasia (suicide) on the list of things he supports that are totally contrary to the Word of God," said Botha.
The Desmond and Leah Tutu Legacy Foundation could not immediately comment on Botha's statement.
Tutu wrote that he had realised he did not want his own life to be artificially prolonged.
"I think when you need machines to help you breathe, then you have to ask questions about the quality of life being experienced and about the way money is being spent. This may be hard for some people to consider."
Tutu wrote that he had worked to help secure dignity for the living.
"Now I wish to apply my mind to the issue of dignity for the dying."
Tutu specified that these were his personal beliefs, and not those of his church.