The 11-month-old is on life support at Great Ormond Street Hospital (GOSH).
President Donald Trump and Pope Francis have voiced their support for the parents. "Thank you", said Yates. Several hospitals in the United States, as well as the Hospital Bambino Gesu near the Vatican have offered to treat Charlie free of charge, should his legal battles be won.
An online campaign to send Charlie to the USA for treatment has raised more than 1.3 million pounds ($1.7 million). Data shows that mice have improved incredibly with the proposed experimental treatment. Speaking of the parents, the statement said: "For them [Pope Francis] prays, hoping that their desire to accompany and care for their own child to the end is not ignored".
But Patrick Mahoney, a pastor at the Church on the Hill in Washington DC, later said he had been able to pray "for a miracle" alongside the parents.
The case will come back to the High Court this afternoon to hear fresh arguments following claims of "new information" from researchers at the Vatican's children's hospital.
New York Presbyterian Hospital and Columbia University Irving Medical Center, meanwhile, told CBS News on Friday it would evaluate Charlie "provided that arrangements are made to safely transfer him to our facility, legal hurdles are cleared, and we receive emergency approval from the FDA for an experimental treatment as appropriate".More news: Government issues official apology, confirms settlement payout to Omar Khadr
More news: Andy Murray aims to be fighting fit for Wimbledon defence
More news: Microsoft patches XP again after "past and threatened nation-state attacks"
"It's disgusting that this decision has been taken out of our hands, it's not just about us knowing best, it's about having other hospitals and doctors saying we want to treat [Charlie] and we think it's the best thing to do".
Charlie can not breathe without a ventilator due to a form of mitochondrial disease which affects the cells responsible for energy production and respiration. "It is because there is no cure that the scientific and medical community have concentrated on pre-conception mitochondrial therapy, and it has been an enormous advance that this is now licensed by the government".
Rare-disease specialists at Bambino Gesu' are working with other global experts to map out an experimental treatment protocol for Charlie, hospital chief Mariella Enoc said.
Lawyers representing Great Ormond Street bosses and a guardian appointed to independently represent Charlie's interests told Mr Justice Francis they were struggling to find any new evidence. Charlie remains on life support, but at any moment the hospital could decide to remove his ventilator.
Ms Yates added: "If he's still fighting, we're still fighting". Even some pro-lifers seem to have been misled by the rhetoric of the hospital and the court system, while the core issue - the natural rights of the parents to make this decision for their child - has been lost. "If he's still fighting, we're still fighting", Mr. Gard said.
@BBCNews How's the guy that's just been run over by the bus live on the news channel outside the high court??