It ruled that that the children's hospital could turn off his life support.
Courts have previously denied Connie Yates and Chris Gard the right to to send their 11-month-old son Charlie Gard to the USA on the grounds it would prolong his suffering without any realistic prospect of it helping.
Bobby Schindler, brother of Terri Schiavo, visited Charlie in Great Ormond Street Hospital, London on Saturday at the invitation of Charlie's parents, Chris Gard and Connie Yates.
Mr Justice Francis, who previously backed Great Ormond Street to end his life support, told the court today: "If there is important new evidence which suggests my judgement should be changed - then I will change it".
Today the High Court will give the parents a final chance to prove why their son should not have his life-support withdrawn.
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.
SKY NEWSFamily spokesman Alasdair Seton Marsden accused the health service of holding Charlie hostage
The judge at London's High Court said the case will be held in full on Thursday.
"We've been requesting this specialised treatment since November, and never asked the hospital, courts, or anyone for anything - except for the permission to go".
The baby's father, Chris Gard, 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?"
The Terri Schiavo Life & Hope Network has advocated for more than 2,500 medically vulnerable patients and families.
But he said he would consider any new evidence and scheduled another hearing in the Family Division of the High Court for Thursday.
It also caught the attention of the Pope and US President Donald Trump who tweeted: "If we can help little #CharlieGard, as per our friends in the United Kingdom and the Pope, we would be delighted to do so".More news: BJP IT Cell secretary arrested for spreading fake news in Bengal