Medics in the two countries came forward with “really supportive” offers of help which have “high success rates”, according to the 12-year-old’s mother Hollie Dance.
Archie has been in a coma with brain damage since he was found unconscious in April. He is being kept alive by a combination of medical interventions, including ventilation and drug treatments, at the Royal London Hospital in Whitechapel, east London.
His parents, Ms Dance and Paul Battersbee, submitted an application to the Strasbourg-based court just a couple of hours before Barts Health NHS Trust was expected to withdraw Archie’s life support.
They are now waiting for the European Court of Human Rights (ECHR) to get back to them.
Speaking outside the hospital, Ms Dance said: “I am hoping that they will step in and give Archie a right to live. I think that he deserves that.”
She added: “If this country can’t treat him or they’re not willing to treat him, where is the harm in allowing him to go to another country?
“There’s other countries that want to treat him and I think that he should be allowed to go.”
She also said a request has been made for Archie to go to a hospice in a “worst-case scenario” but said the hospital has “brutally” said no.
On Tuesday evening, Ms Dance said the trust would begin to withdraw the life support at 11am on Wednesday unless the family submitted the application to the ECHR by 9am.
On Wednesday morning, Alistair Chesser, chief medical officer for Barts Health NHS Trust, said: “Our deepest sympathies remain with Archie’s family and we aim to provide the best possible support to everyone at this difficult time.
“As directed by the courts, we will work with the family to prepare for the withdrawal of treatment, but we will make no changes to Archie’s care until the outstanding legal issues are resolved.”
In a statement, the ECHR said it has received an application for interim measures and that it is being processed.
Ms Dance spoke of the devastation she is experiencing, saying: “I’m not going to lie, I am broke, and at some point I am going to need serious therapy, but I haven’t got time to think about me at the minute.
“This is a serious fight for my son’s life and I’m up against the biggest system and a trust that I haven’t got time to break down at the moment.”
Archie was found unconscious at his home by his mother on 7 April and has not regained consciousness since.
She believes he was taking part in an online challenge.