Charlie Gard's parents have been given a second chance to save their sick baby.

A British court has given the parents of terminally ill 11-month-old Charlie Gard a fresh chance to present evidence as to why they should be allowed to take their son to the United States for experimental treatment.

After an emotionally charged hearing in London’s High Court, during which Charlie’s mother wept in frustration and his father yelled at a lawyer, Judge Nicholas Francis gave them 48 hours to present new information in the case.

Charlie suffers from mitochondrial depletion syndrome, a rare genetic disease that has left him brain damaged and unable to breathe unaided. His parents want to take him to the US for experimental therapy, which they say offers their son a chance of improvement.

The case, which has drawn international attention, returns to court on Thursday.

But the judge insists there has to be "new and powerful" evidence to reverse earlier rulings that barred Charlie from travelling overseas for treatment and authorised London's Great Ormond Street Hospital (GOSH) to take him off life support.

"There is not a person alive who would not want to save Charlie," Francis said. "If there is new evidence I will hear it."

British and European courts have sided with the hospital's decision that the 11-month-old's life support should end, saying therapy would not help and would cause more suffering.

GOSH applied for another court hearing because of "new evidence relating to potential treatment for his condition."

The evidence came from researchers at the Vatican's children's hospital and another facility outside of Britain.

The application came after both Pope Francis and President Donald Trump fuelled international attention to the case, with hospitals in Rome and the US offering to provide Charlie the experimental therapy.

The case pits the rights of parents to decide what's best for their children against the authorities with responsibility for ensuring that people who can't speak for themselves receive the most appropriate care.

Charlie's parents, Chris Gard and Connie Yates, have received wide public support, while right-to-life groups have intervened in their cause.

A petition supporting Charlie's right to treatment has garnered around 350,000 signatures and more than 1.3 million pounds ($A2.2 million) have been raised online for his case.