The Church of England has declared organ donation to be a Christian duty, in keeping with giving oneself and one's possessions freely.
Body parts should not be viewed as the person himself, the Church says
Body parts should not be mistaken for the person themselves, and the best way to treat them reverently is to use them to heal others, the Church said.
It was taking part in a House of Lords consultation on whether there should be an EU-wide position on organ donation.
The Church said it would welcome the creation of a European donor pool.
But its Mission and Public Affairs Division would not be drawn into setting out a position on whether an opt-out system, in which everyone is considered a donor unless they state otherwise, was preferable to an opt-in, when people state their wish to donate.
This was "not a question on which Christians hold a single set of views", said Reverend Tom Butler.
"The opt-in system reflects our concern to celebrate and support gracious gifts, freely given," he said.
"The opt-out approach stresses Christian concern for human solidarity and living sacrificially for others."
The UK is currently considering switching from an opt-in to an opt-out system, in the hope of meeting a chronic organ shortage.
Making this change has dramatically increased the number of organs available for transplant in some - although not all - of the countries which have done so.
The Church said that were there to be an EU-wide donation policy, member states would have to adopt the same system of consent.
"Member states will need to ensure that there is a balance between the organs they can provide and those their citizens need for transplant otherwise some nations will be jeopardised and worse off than hitherto."
Many faiths support the principle of organ donation, including the Roman Catholic Church, although they are thought unlikely to support the notion of it being a "duty".