Chris Gard and Connie Yates have until Tuesday to lodge an appeal against a High Court judgement last month that they could not take their son to the United States for a treatment trial.
Chairman of the Department for Christian Responsibility and Citizenship of the Bishops' Conference of England and Wales, Archbishop Peter Smith said: "Our heartfelt prayers and support are with baby Charlie and his parents and family, as well as with those caring for him."
Archbishop Peter Smith speaks on the case of baby Charlie Gard and his life-support treatment. Find more here https://t.co/9eMF9vFV2t
— Catholic Church (@catholicEW) May 2, 2017
Last month, Judge Mr Justice Francis sided with staff at Great Ormond Street Hospital in London who said life-support treatment should be ended for Charlie, who suffers from a brain damage and a rare genetic condition.
Archbishop Peter went on to say: "The tragic situation of baby Charlie Gard is truly heartrending, not least, of course, for his parents and family.
"Those responsible for his medical care in the UK believe they have done all they can to help him.
"It is completely understandable, nonetheless, that his parents should also want to pursue every possible chance of extending his life, even when this carries no guarantee of success and would require transfer to the United States."
Charlie, who is nine months old, was born with a type of mitochondrial disease, which causes progressive muscle weakness and brain damage.
US specialist had offered nucleoside therapy; however, the judge said the experts acknowledged the treatment would not undo Charlie's brain damage.
Archbishop Peter added: "Where medical treatment becomes disproportionate to any possible benefit, proper palliative care for a sick person must be maintained.
"Such care must include the provision of nutrition and hydration which is neither treatment nor medicine, unless this itself becomes overly burdensome.
"We should never act with the deliberate intention to end a human life, including the removal of nutrition and hydration so that death might be achieved.
"We do, sometimes, however, have to recognise the limitations of what can be done, while always acting humanely in the service of the sick person until the time of natural death occurs."