Although circumcision is widely done for religious and cultural reasons, a bill in the Icelandic parliament calls for someone to imprisoned for up to six years if the procedure is not done solely for medical reasons.
The proposed bill states that "Anyone who... causes damage to the body or health of a child or a woman by... removing sexual organs shall be imprisoned for up to six years."
Cardinal Reinhard Marx, president of the Catholic Church in the European Union (COMECE), has attacked the idea.
He said in a statement: "Protecting the health of children is a legitimate goal of every society, but in this case this concern is instrumentalised, without any scientific basis, to stigmatise certain religious communities. This is extremely worrying.
"COMECE considers any attempt on the fundamental right to freedom of religion as unacceptable.
"The criminalisation of circumcision is a very grave measure that raises deep concern."
COMECE said although Iceland is not part of the EU, it has with it privileged relations which imply the respect of certain principles and obligations.
Supporters of the bill have expressed concern that male circumcision is not carried out with anaesthesia and is conducted by religious leaders, not doctors.
They are also worried about the "high risk of infection... that may lead to death" because the procedure is usually done in homes that have not been sterilised.
The bill adds that although parents have the right to give their child a religious upbringing, it should not supersede the rights of the child.
Lawmakers have suggested that boys can be circumcised for religious or cultural reasons when they have a full understanding of the procedure.
The bill has support across political parties in Iceland and is due for its first reading in parliament.
Female gender mutilation was banned in Iceland in 2005.
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