The government has asked judges to consider an urgent request from a United Nations committee to continue treating the 12-year-old while the case is investigated.
The Court of Appeal hearing is scheduled for 11 a.m., three hours before the end of care at 2 p.m.
Archie was discovered unconscious at his home in Southend, Essex, on April 7.
He has never regained consciousness, and his mother, Hollie Dance, believes he was participating in an online challenge.
Archie, who is being treated at the Royal London Hospital in east London, is scheduled to have his life support turned off on Monday afternoon.
Doctors at the Royal London Hospital, where Archie is being treated, have determined that he is brain-stem dead and that it is in the best interests of the child to discontinue treatment.
Judges on the Appeal Court ruled last week that doctors could legally disconnect his ventilator.
It comes after two High Court judges agreed with doctors and said that life-sustaining treatment could be discontinued.
Archie’s family petitioned the UN Committee on the Rights of Persons with Disabilities (UNRPD) to hear the case, claiming the UNRPD had a protocol that allowed individuals and families to “complain about violations of disabled people’s rights.
The committee requested that Archie’s life support be maintained while it considered his family’s application, which the government has now granted.
A legal “stay” has also been imposed to prevent treatment from being withdrawn until Monday at 1pm.
Ms Dance expressed relief that the government had taken the UN’s intervention seriously.
“This was not a’request,’ but a UN interim measures injunction,” she explained.
“Being told that Archie’s life support will be removed tomorrow at 2 p.m. has been terrifying.” We were already broken, and not knowing what would happen next was excruciating.”
The Christian Legal Centre is a campaign organisation that is assisting Archie’s parents.
Archie Battersbee suffered brain damage in a home incident on April 7 and has not recovered consciousness.
Our deepest sympathies are with Archie’s family at this difficult time,” said Alistair Chesser, chief medical officer for Barts Health NHS Trust, which runs the hospital.
“The plan to withdraw treatment will proceed unless the court directs otherwise,” we understand a court hearing will take place on Monday morning.
Because the UK had signed the optional protocol to the Convention on the Rights of Persons with Disabilities, the UN could ask the government to postpone the withdrawal of life support while an investigation was conducted, according to Christian Concern.
“We recognise this is an exceptionally difficult time for Archie Battersbee’s family, and our thoughts are with them,” a spokesman for the Department of Health and Social Care said.
The government requested that the High Court consider the UN Committee on the Rights of Persons with Disabilities’ request as soon as possible.”