Sir Andrew McFarlane, presiding over the case at the Court of Appeal, said the Convention on the Rights of Persons with Disabilities, which the UN committee based its request on, is an "unincorporated international treaty".
He said: "It is not part of the law of the United Kingdom... and it is not appropriate for this court to apply an unincorporated international treaty into its decision-making process."
"Every day that (Archie) continues to be given life-sustaining treatment is contrary to his best interests and, so, a stay, even for a short time, is against his best interests," he added.
Sir Andrew said Archie's case was "stark" as "his system, his organs and, ultimately, his heart are in the process of closing down".
Sky News