"If there is important evidence which suggests that I should change my decision then I will change it," Judge Nicholas Francis told the packed courtroom in central London.
Francis, who had previously ruled that life support for 11-month-old Charlie Gard should be withdrawn, indicated that he would not be making a ruling today.
Emotions ran high at the hearing and the boy's parents, Connie Yates and Chris Gard, walked out of the courtroom over a disagreement about what they had said in a hearing back in April.
Earlier this week, the boy's parents submitted a petition of over 350,000 signatures to the hospital, demanding that they be allowed to take him to the United States for treatment.
A Vatican-run hospital in Rome has also said treatment may be possible.
But the London hospital has so far stood by its opinion that Gard's rare form of mitochondrial disease, which causes progressive muscle weakness in the heart and other key organs, was not treatable.
But doctors said it was "right to explore" any new evidence and that they were seeking the court's view.
The baby's father accused the hospital of lying at a preliminary hearing on Monday, shouting at the barrister representing the facility: "When are you going to start telling the truth?"
Gard's parents have lost a series of appeals in British courts and the European Court of Human Rights in Strasbourg and had no further legal recourse.
But the case drew international attention last week after the pope expressed his support for the baby's parents, saying he hoped doctors would allow them to "care for their child until the end".
A US specialist is to present evidence via video conference later.
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