While encouraging people to join the donor register, Christian Action Research and Education (CARE) said it remained "deeply concerned" by a proposal to introduce presumed consent.
Spokesperson James Mildred told Premier the idea raises ethical questions and research investigating its effectiveness has been inconclusive.
He said: "It fundamentally alters the nature of organ donation, which should be a genuine beautiful gift; you voluntarily chose to give your organs."
The family of a deceased person would still be consulted about organ donation under the plans, which could come into force in 2020.
Some 180,000 people opted out of organ donation in Wales in the twelve months after an opt-out system was introduced three years ago.
CARE believes a more effective way of boosting organ donations would be to have specialist nurses who can explain the process to a deceased person's family.
Mr Mildred added: "Simply by having a short conversation with your loved ones and telling them about your wishes can actually increase the likelihood that, if you want your organs to be donated, they will be donated."
Unveiling its consultation - which ended last December - the Government said: "The Government wants views from as many people as possible on plans to make it easier for people to give consent to be an organ donor."
Click here to listen to Premier's John Pantry and Rosie Wright speaking with James Mildred at CARE:
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