Specialists caring for Tafida Raqeeb at the Royal London Hospital in east London said further treatment would be futile because the youngster has permanent brain damage, is in a minimally conscious state and has no chance of recovery.
Tafida's parents, who live in Newham, east London, want to move her to Gaslini children's hospital in Genoa, and have organised funding.
Her mother, solicitor Shelina Begum, and father, construction consultant Mohammed Raqeeb, said doctors there would keep providing life-support treatment until Tafida was diagnosed as brain dead.
They said Tafida, who has a British-Bangladeshi background, is from a Muslim family and Islamic law only allows God to end life.
Speaking after the ruling, Bishop John Sherrington, lead bishop for life issues for the Catholic Bishops' Conference of England and Wales said: "I welcome today's ruling which has taken account of the wishes of Tafida's parents and their innate urge to do all they can to help their daughter in what are truly tragic circumstances. The heart-breaking illness of Tafida Raqeeb and the distress which the illness of a child causes parents touches the hearts of many people.
"I trust that all the medical professionals will cooperate to continue to give her the best possible care and appropriate treatment. Such international cooperation is essential good practice in the care of tragically difficult lives. I will keep these professionals in my prayers.
"I, along with many others, have held this family in my prayers and will continue to pray that Tafida and her parents are strengthened by the presence and mercy of God, and by the support of all who know and love her."
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