Video report by ITV News Correspondent Rebecca Barry
Charlie Gard's father interrupted a court hearing over his son's future by shouting at a barrister "When are you going to tell the truth?"
The 11-month-old's parents staged an emotional intervention as a judge considers claims of fresh medical evidence to decide if the critically-ill baby should be allowed to travel abroad for experimental treatment.
Mr Justice Francis, who ruled in April that ending life-support treatment would be in Charlie's best interests, said he could potentially revise his decision if "new and powerful" evidence came to light.
His parents said that the latest round of their legal battle had given them new hope he would be allowed to undergo treatment for a severe genetic condition that has left him brain damaged and dependent on life support.
Speaking afterwards, they vowed they would keep fighting until the end in a statement read out by a family friend.
During today's hearing, Charlie's father Chris Gard accused a lawyer representing doctors at Great Ormond Street Hospital of lying about the 11-month-old's condition.
Charlie's mother, Connie Yates, also spoke out, saying: "He is our son. Please listen to us."
Doctors have said there is no realistic chance that Charlie can stage any meaningful recovery and that further treatment may cause him pain.
His parents say that his condition is better than doctors admit and there is nothing to be lost by trying to offer him therapy.
During the hearing, lawyers representing the family said there was "encouraging" evidence about the therapy in America, which suggests a "small chance" of brain recovery.
The family's legal team also suggested that another judge should analyse any fresh evidence.
But Mr Justice Francis disagreed. "I did my job," he said. "I will continue to do my job."
He adjourned the hearing until Thursday and said Charlie's parents should set out any new evidence.
"There is not a person alive who would not want to save Charlie," he said.
"If you bring new evidence to me and I consider that evidence changes the situation ... I will be the first to welcome that outcome," he added.
Outside the court, a small group of supporters held banners with "Save Charlie Gard" slogans.
Charlie has a rare, degenerative genetic condition which affects the cells responsible for energy production and respiration and leaves him unable to move or breathe without a ventilator.
Doctors had previously won an order to say Charlie's life support should be turned off in a case that went all the way to the European Court of Human Rights.
On Friday, GOSH announced it hadapplied to return to the court "in light of claims of new evidence relating to potential treatment for his condition" in the wake of an offer from a US hospital to ship an experimental drug to the UK to help treat Charlie.
Earlier, Ms Yates said the interest of the Pope and US President Donald Trump in Charlie's case has "saved his life so far".
She said the family have gained support from seven specialist doctors in four countries, including England, after a petition that has gained 350,000 signatures.
But she said it was the high-profile interventions from the Vatican and Washington that has prolonged their campaign.
"There are a lot of people that are outraged by what is going on. We have got new evidence now so I hope the judge changes his mind."
Ms Yates said she and Charlie's father, Chris Gard, are not fighting hospital doctors to simply prevent the switching off of their son's life support.
"Sometimes parents are right in what they think," she said. "We expect that structural damage is irreversible but I have yet to see something which tells me my son has irreversible structural brain damage," she said.