The parents, Connie Yates and Chris Gard, hold out hope that the treatment could improve eleven-month-old Charlie's condition but courts have been blocking the move.
Gard's parents, who submitted a petition of over 350,000 signatures demanding that they be allowed to take him to the United States for treatment, attended the hearing at the High Court in London.
Great Ormond Street Hospital applied for a new hearing "in light of claims of new evidence relating to potential treatment" for baby Charlie, who has a genetic disease that causes progressive muscle weakness.
Specialists at Great Ormond Street Hospital in London, where Charlie is being cared for, have said therapy proposed by a doctor in America is experimental and would not help.
The couple interrupted the hearing, with Mr Gard shouting: "When are you going to start telling the truth?" at a barrister representing Great Ormond Street bosses.
Ms Yates told the judge: "He is our son".
The parents begged judges to allow Charlie to receive a "miracle" treatment, insisting "we don't want him in the ground, we want him riding a bike".
GOSH's decision to go back to court came after researchers at two global healthcare facilities said they had "fresh evidence" about their proposed experimental nucleoside therapy.
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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 United States, following a similar ruling by the UK's supreme court.
The boy is battling mitochondrial depletion syndrome, a rare genetic disease that affects his energy production and respiration, and the court had been expected to decide today whether the wishes of Charlie's parents to pursue the experimental treatment will be granted. The hospital argues that the therapies are "unjustified" and said the treatments being offered are not a cure.
"Not only that, but they said it would be futile and would prolong Charlie's suffering".
Lawyers representing Charlie's parents said evidence indicated a "small chance" of brain recovery.
She said no further imaging of Charlie's brain had been carried out since the April ruling.
Grant Armstrong QC, representing the couple, said the doctor wanted the court to know that he believed the figure to be a "conservative estimate regarding clinical outcome".
The couple want a High Court judge to make a fresh analysis of their case.
Lidington said Sunday that the government won't play a role in deciding Charlie's medical treatment, and that today's hearing will be decided by judges acting "independent and dispassionately" based on the facts of the complicated case, according to a report by The Associated Press.