The family of Archie Battersbee have been denied permission to take their case to the UN by the Court of Appeal.
The court previously upheld a decision by the High Court to withdraw life support treatment for the 12-year-old.
Young Archie has relied on mechanical ventilation since April 7 and has been in a “comatose state” after suffering “catastrophic” brain damage in an accident at home three months ago.
Archie’s parents, Hollie Dance and Paul Battersbee, who are separated but both live in Southend, Essex, had asked judges at the European Court of Human Rights to intervene after losing the latest round of a treatment fight in London.
Three Court of Appeal judges upheld a ruling on Monday by a High Court judge who had decided that doctors could lawfully stop treating Archie.
His parents argued that Mr Justice Hayden had made errors after the High Court hearing.
They have now made an urgent application to the Supreme Court after today's Court of Appeal denial.
Barts Health NHS Trust want to withdraw treatment and were given permission to do so following best interest proceedings in the High Court.
However, Archie's parents claim this is against Archie's wishes and say the decision breaches Articles 10 and 12 of the UN Convention on the Rights of People with Disabilities, as well as Article 6 of the UN Convention on the Rights of Children.
The High Court had previously found that Archie can't feel pain and so his current treatment regime does not cause him any pain or distress.
Damage to his spinal cord could also prevent his breathing independently regardless of any damage to his brain, it's claimed.
The family's legal team argues that withdrawing ventilation will therefore result in his certain death, with mum Holly releasing a video of her son she claims provides 'new' evidence he is still breathing on his own.
She insists Archie is able to breathe independently of a respirator as the Christian Legal Centre - which is supporting the family's case - and circulated a video which they want to submit as evidence.
The clip shows Archie on an emergency room monitor displaying his respiratory rate - which is set by a ventilator.
Following the Court of Appeal ruling on Monday, the High Court order for treatment removal had been stayed for two days pending any application to international tribunals, and it's reported that the stay has been granted until Thursday at 2pm.
Judges have heard that Archie was found unconscious with a ligature over his head on April 7.
His mum thinks he might have been taking part in an online challenge and the youngster has not regained consciousness since.
Doctors treating Archie at the Royal London Hospital in Whitechapel, east London, think he is brain-stem dead and say continued life-support treatment is not in his best interests.
Another High Court judge, Mrs Justice Arbuthnot, initially considered the case and concluded that Archie was dead.
But Court of Appeal judges upheld a challenge by his parents against decisions taken by Mrs Justice Arbuthnot and said the evidence should be reviewed by Mr Justice Hayden.
Meanwhile, appeal judges were told on Monday that Archie's father, Paul Battersbee, who is in his 50s, was feared to have suffered a heart attack or stroke outside a courtroom at the Royal Courts of Justice in London.
