A spokesman for Hollie Dance and Paul Battersbee said Archie’s parents wanted the UN Committee On The Rights Of Persons With Disabilities to consider the youngster’s case.
The move comes despite a High Court judge said ending treatment is in Archie’s best interests.
The youngster’s parents, who are separated but both live in Southend, Essex, failed to persuade Court of Appeal judges to overturn that ruling and Supreme Court justices have refused to intervene.
Archie’s parents are being support by a campaign organisation called the Christian Legal Centre.
A spokesman for the centre announced its latest move and said it had made a “last-ditch application”.
Archie Battersbee, 12, has not regained consciousness Hollie Dance
The parents of Archie Battersbee, Paul Battersbee and Hollie Dance Victoria Jones
They said: “Archie’s parents want the UN committee to consider Archie’s case, arguing it has a protocol that allows ‘individuals and families’ to make complaints about violations of disabled people’s rights.
“The family argue that stopping treatment would be in breach of the UK’s obligations under Articles … of the UN Convention on the Rights of People with Disabilities, and under an Article of the UN Convention on the Rights of Children.”
Archie’s parents have asked hospital bosses to continue treatment until the UN has considered the case.
Judges have heard that Ms Dance found Archie unconscious on April 7. The youngster has not regained consciousness.
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.
A 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 a different High Court judge, Mr Justice Hayden.
Miss Dance said: “Words cannot describe how devastated we are.
“The pressure put on us from the beginning to rush through the process of ending Archie’s life has been disgraceful.
“All we have ever asked for is for more time.
“The urgency from the hospital and the courts is unexplained when other parties have been happy for us to have more time.
“I don’t believe there is anything ‘dignified’ about planning Archie’s death.
“For me, this would be the most traumatic outcome.
“Parents need support not pressure.
“It is exhausting what we have been through.
“We should not have to endlessly battle the hospital in the courts for what we believe is right for Archie.
“Top judges have told us, however, that this is the law, if this so, the law must change.
“We will continue fighting for Archie, we will not give up and now await the response from the UN committee.”
Hollie Dance and Archie Battersbee Handout
Archie Battersbee was found unconscious on April 7 Handout
The Christian Legal Centre spokesman added: “The UK has an obligation under international human rights law to comply with interim measures indicated by the committee.
“That obligation comes from the Optional Protocol to the UN Convention on the Rights of Persons with Disabilities.
“The Optional Protocol creates an enforcement mechanism for the convention, i.e. the committee with power to monitor states’ compliance, consider individual complaint, and issue interim measures.
“A number of UN conventions have similar Optional Protocols.
“The UK has chosen to opt into some but not the others.
“In the case of disability rights, the UK Government has taken a considered decision to join the Optional Protocol and to be bound by the decisions of the committee.
“The NHS trust is an emanation of the UK state. We therefore expect the Government and the trust to honour its international human rights obligations.”