The Great Ormond Street Hospital has argued that the treatment overseas sought by Charlie's parents, Chris Gard and Connie Yates, would not help. GOSH determined that he should be taken off his life support. She said Charlie, who has a rare mitochondrial disease, was able to derive pleasure from life and still "enjoyed his tickles".
Grant Armstrong, representing Charlie's parents, said there was "encouraging" evidence from researchers at the Vatican's children's hospital about an experimental treatment. "We're talking about world-class hospitals, first in the field, and that is what they prefer", she said.
Charlie's parents were overcome with emotion during Monday's hearing.
They received another boost this week when Donald Trump voiced his support for their cause, pledging to find a way for Charlie to receive treatment in the US.
The High Court in England ruled that Great Ormond Street Hospital-where he has been receiving treatment-had the right to remove life support and allow him to die.
Under a High Court ruling, GOSH is forbidden from allowing Charlie to be transferred for nucleoside therapy anywhere.
But on Friday the hospital applied to the High Court for the fresh hearing "in light of claims of new evidence relating to potential treatment for his condition".
The petition in question urged the hospital to allow Charlie to go to the US for experimental treatment, in spite of earlier court rulings and hospital opinions that Charlie Gard should be allowed to "die with dignity".
"I am holding my hands up, I say my prayers over my son every night and I am thankful that he is on that medication".
At the end of June, the European Court of Human Rights rejected an appeal by Charlie's parents that he be allowed to undergo the experimental treatment in the U.S., following a similar ruling by the UK's supreme court.
He told them he wanted to know what had changed with the 11-month-old's condition and said he would make decisions on the basis of "clear evidence".
They said there was a "good prospect" of further evidence producing a different result.
However, the treatment has never been used on either mice or humans with the type of mitochondrial disease from which Charlie suffers, according to court documents.
Charlie has a faulty RRM2B gene, which affects the cells responsible for energy production and breathing, meaning he can not move or breathe without a ventilator.
When Charlie's doctors asked for evidence that the therapy might help, Dr I said: "There is no direct evidence, but there is a theoretical scientific basis for saying it could". The hospital also offered to send the drug to Great Ormond Street Hospital - the British hospital where Charlie is being treated - if approved, the Post added.