The Court of Appeal is standing by a previous judgment that it is in Archie Battersbee's "best interests" to die.
A last minute hearing was held today at the request of the government after the United Nations Committee on the Rights of Persons with Disabilities (UN CRPD) asked for a temporary stay on removing Archie's life support while it considers his case.
Sir Andrew McFarlane, President of the Family Division of the Court of Appeal, has rejected the UN CRPD's request.
Handing down judgement, Sir Andrew described the UN CRPD convention as an "unincorporated international treaty" and said that it would "not appropriate for this court to apply it into its decision-making process".
The judgment maintains that "if this court was to cede to the parents' application, the court would be acting contrary to Archie's 'best interests'", although he added that the intervention by the UN CRPD is "to a degree untrod ground".
"The question of a stay is not dictated by the fact that a request has been made by [the UN CRPD]," he said.
The judgment gives Archie's parents until 12pm on Tuesday to appeal to the Supreme Court.
Archie's mother, Hollie Dance, said: "We continue to be shocked and traumatised by the brutality of the UK courts and the hospital Trust.
"Our wishes as parents continue to be trampled on and ignored. We do not understand the urgency and rush to end life-support.
"The hospital Trust has at no point given us time to come to terms with what has happened. This is no way for a compassionate society to treat a family in our situation. We will continue to fight for Archie."
Andrea Williams, chief executive of the Christian Legal Centre, which is supporting Archie's family, said:"What Archie's case has shown is that systematic reform is needed to protect the vulnerable and their families in end-of-life matters. Legislation must be passed reforming the system.
"Archie's case stands in the gap. The precedent his case sets can go an incredibly long way to fixing a system which has no room for error.
"We will stand with them as they appeal to the Supreme Court."