The terminally ill boy's parents say "he deserves a chance" as the case returns to the High Court following "new information".
The 11-month-old is on life support at Great Ormond Street Hospital and has been at the centre of a long legal battle over his medical care.
His parents Chris Gard and Connie Yates want him to get nucleoside therapy, which is available in the US, but doctors at the hospital say the treatment is "unjustified".
Charlie's parents have been stopped from taking him across the Atlantic by a High Court ruling.
Judges in the High Court, Court of Appeal and Supreme Court have all sided with the doctors, while the European Court of Human Rights said it would not intervene.
This afternoon, the case returns to the High Court to hear fresh arguments following "new information" from researchers at the Vatican's children's hospital.
Charlie has a faulty RRM2B gene, which affects the cells responsible for energy production and breathing, meaning he cannot move or breathe without a ventilator.
The case has prompted intervention from the Pope and US President Donald Trump, who offered support for the baby, with hospitals in both countries offering to take Charlie.
Professor Neena Modi, president of the Royal College of Paediatrics and Child Health, said in an open letter that "only the family, the doctors treating Charlie, and now the legal teams involved know the details of complex issues that define his situation".
"These issues - unknown to us and all those voicing opinions - will have been considered very carefully in reaching any decision.
"This is why interventions by external agencies or individuals, no matter how well-intended, are unhelpful."
Prof Modi said decisions on withdrawing life support are "not made lightly" and don't often reach the courts.
"When situations are hopeless or unbearable or life is limited, the focus of care rightly shifts to ensuring death is pain-free, dignified, and in the presence of loved ones.
Charlie's parents spoke outside Great Ormond Street on Sunday, as a petition of more than 350,000 signatures was presented calling on doctors to allow their son to travel to the US.
Ms Yates said: "He's our son, he's our flesh and blood. We feel that it should be our right as parents to decide to give him a chance at life.
She said they had received support from doctors from all over the world, as well as the UK.
Ms Yates said the oral medicine they want for Charlie has an "up to 10% chance of working" and has "no known major side effects".
Mr Gard said there is no evidence Charlie has "catastrophic brain damage", and added: "He should have had this chance a long time ago now."