A High Court judge has given doctors permission to provide only palliative care to 12-month-old Isaiah Haastrup, against the wishes of his parents, Lanre Haastrup and Takesha Thomas.
Mr Justice MacDonald analysed Isaiah's case at the Family Division of the High Court in January after specialists at King's College Hospital in London said providing further intensive care treatment was futile and not in the youngster's best interests.
Three Court of Appeal judges upheld his ruling.
Mr Haastrup and Miss Thomas, who are both in their 30s and from Peckham, south-east London, say they have spelled out their case in a written application to the European Court of Human Rights in Strasbourg, France.
A spokesman for King's College Hospital said medics would continue treating Isaiah until European judges had made a decision.
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