The parents of 12-year-old Archie Battersbee have said they want the United Nations to consider their case to keep him alive.
It comes after the Court of Appeal earlier this week upheld the High Court's decision to withdraw life-support treatment for the brain-damaged child.
His father Paul Battersbee and mother Hollie Dance say the UN has a protocol that allows "individuals and families" to make complaints about violations of disabled people's rights.
They claim the UN could ask the UK government to delay the withdrawal of life support while a complaint is investigated.
Archie has relied on mechanical ventilation since being admitted to hospital on 7 April, after being found with a ligature around his neck at home.
Doctors treating him 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.
Barts Health NHS Trust wants to withdraw treatment and was last week granted permission to do what the High Court ruled was best for Archie.
On Monday, Court of Appeal judges said doctors could lawfully stop providing the treatment and the youngster could be disconnected from a ventilator.
Archie's family say they will now apply to the Supreme Court in order to pave the way for the case to be heard at the UN.
The family argue that withdrawing treatment is contrary to the boy's clearly expressed wishes.
And his relatives also claim stopping it would be in breach of the UK's obligations under Articles 10 and 12 of the UN Convention on the Rights of People with Disabilities, and Article 6 of the UN Convention on the Rights of Children.
These international obligations say states must take all necessary measures to ensure disabled people enjoy equal rights and that governments should do all they can to prevent the deaths of children and young people.
The High Court had found that Archie cannot feel pain and therefore his present 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.
The family's legal team argues that withdrawing ventilation will therefore result in his certain death.
Judges have heard that Hollie Dance found her son unconscious with a ligature over his head. She thinks he might have been taking part in an online challenge.
The youngster has not regained consciousness.
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.
Sky News understands the stay has been granted until Thursday at 2pm.
Meanwhile, Mr Battersbee, who is aged in his 50s, has left hospital after being taken ill shortly before the Court of Appeal ruling.