Pope Francis has called for the parents of terminally-ill Charlie Gard to be allowed to "accompany and treat their child until the end".
It comes as Chris Gard and Connie Yates are spending the last days of their 10-month-old son's life with him, after being given more time before his life-support is turned off.
In a statement, the Vatican press office said the pope "is following with affection and sadness the case of little Charlie Gard and expresses his closeness to his parents. For this he prays that their wish to accompany and treat their child until the end is not neglected".
Charlie, who suffers from a rare genetic condition and has brain damage, is being cared for at Great Ormond Street Hospital (GOSH).
The little boy has been at the centre of a lengthy legal battle between his parents, who wanted him to undergo a therapy trial in the US, and specialists at the hospital who said the treatment was experimental and would not help.
On Friday a picture of the couple sleeping on either side of their son in hospital was posted on their Twitter account alongside the hashtags #jesuisCharlieGard #charliesfight #letcharliegohome.
The couple released an emotional video a day earlier saying they had been told Charlie would die on Friday.
They said they had been denied their final wish to be able to take their son home to die and felt "let down" after losing their legal fight.
The hospital later confirmed it was "putting plans in place for his care".
Charlie's plight has touched many people and the family received donations totalling more than £1.3 million to take him to the US for therapy.
Monsignor Vincenzo Paglia of the Vatican's Pontifical Academy for Life issued a statement saying: "Dear Charlie, dear parents Chris Gard and Connie Yates, we are praying for you and with you."
He also drew criticism for saying the parents' wishes should be respected, but that they must also be helped to understand the "unique difficulty of their situation".
Campaigners have pledged their support to the family on social media using hashtags and blue heart emoticons.
Charlie's parents, both in their 30s and from Bedfont, west London, had asked European court judges in Strasbourg, France, to consider their case after judges in the High Court, Court of Appeal and Supreme Court in London ruled in favour of GOSH doctors.
But last week the European Court of Human Rights refused to intervene.
On Sunday, campaigners carrying a banner that said "It's Murder" gathered outside Buckingham Palace to protest against the court's decision.
Other posters with pictures of Charlie said "Where there's life, there's hope" and "parental rights".