On Friday, Great Ormond Street Hospital for Children, where Charlie is being cared for, said it wanted the court to hear new evidence relating to the case, "in light of fresh evidence concerning potential treatment".
But doctors said it was "right to explore" any new evidence and said they were seeking the court's view. "I will be the first to welcome that outcome".
Emotions ran high during the hearing with ITV News also reporting that the child's father yelled at a barrister representing Great Ormond Street Hospital (GOSH), where his son is being treated, "when are you going to start telling the truth?"
The hospital gave no details of the new medical information, but British media and the infant's parents, Chris Gard and Connie Yates, have highlighted treatment at several USA hospitals.
The courts had ruled that keeping the baby on life support would only prolong his suffering as there was no hope of him recovering from his extremely rare form of mitochondrial disease, which causes progressive muscle weakness, including in key organs such as the heart. As a result, he is unable to move his arms or legs or breathe unaided. Britain's justice secretary says the government won't play a role in deciding the medical treatment of a terminally ill baby whose parents want to take him to the US for experimental treatment.
Parents of Charlie Gard, Connie Yates and Chris Gard pose for the media ahead of delivering a petition with more than 350,000 signatures to Great Ormond Street Hospital in London, Sunday, July 9, 2017.
The hospital requested a review of the justice after the publication of a letter from the Bambino Gesu Hospital in the Vatican, which presented its research and recommended that the Great Ormond Street Hospital "reconsider" its position.
BBC Radio 4 early Monday that her son still has a chance of surviving thanks to the intervention of Trump and the pontiff, who turned their fight "into an worldwide issue".
"It is our son, our flesh and our blood".
The official also said the president wants to be helpful without placing undue pressure on the family.
"I have to decide this case not on the basis of tweets, not on the basis of what might be said in the press, or to the press", Judge Francis said, acknowledging public interest surrounding the case.
He said: It seems that if he remains at Great Ormond Street it seems that nearly certainly his life support will be withdrawn and clearly he is likely then to die. After the hospital's refusal, the parents filed a case in the European Court of Human Rights that ruled June 27 the boy could not be taken to the USA and should be removed from life support. The document had been signed by 370,000 people.