Archie Battersbee’s family claim they have been refused a request for the brain-damaged boy to be moved to a hospice for life support to be turned off.
They also say two other countries have offered to care for their son, who British doctors and courts say should be taken off treatment.
The High Court has given medics permission to stop treating the 12-year-old despite his parents’ wishes, saying this was in Archie’s best interests.
A London hospital was set to turn off life support from 11am on Wednesday, following weeks of legal disputes over his care.
But Hollie Dance, his mother, said it had agreed to hold off while the European Court of Human Rights considered the family’s latest bid for a delay - submitted the same morning.
She said the family wanted Archie to go to a hospice in the “worst-case scenario” and had asked the hospital to allow this.
“This hospital brutally said no,” Ms Dance told reporters outside the Royal London Hospital on Wednesday morning.
“The courts are really focusing on the word dignity. What is dignified in dying in a busy hospital room, full of noise, with the door open [and] people coming in and out continuously, when Archie could be in a very peaceful garden with squirrels and wildlife running arund to have his life support withdrawn there?
“If they really want to focus on this word dignity, I think that option seriously needs to also be looked at.”
A family friend described his conditions in the hospital on Tuesday, saying there were “seven or eight” security guards outside the brain-damaged boy’s room.
“If this is Archie’s last couple of days it needs to be peaceful and it needs to be a calm atmosphere, and it’s the complete opposite really,” Ella Carter told reporters outside the London hospital.
Ms Dance said on Wednesday the family had been offered treatment in Italy and Japan for their son.
“If this country can’t treat him or they are not willing to treat him, what is the harm of going to another country?” she said.
Ms Dance said she was “running on empty” and Tuesday was a “very down day”.
“Today I’m back again and I’m fighting,”she said, adding: “We are going to fight for the right for my son to live.”
Archie suffered a brain injury in April during an incident at his home in Southend, Essex, which his mother believes may have been linked to an online challenge.
The 12-year-old boy has not regained conciousness since and has been kept in intensive care at the Royal London Hospital in Whitechapel.
While the hospital trust have been granted permission to switch his life support off from Wednesday morning, his parents said they would submit a last-minute application to the European Court of Human Rights in a bid to postpone the withdrawal of his life support.
It comes after they exhausted all routes of appeal to the High Court ruling in the UK. They also lost a legal case over a UN request to delay withdrawing treatment while a committee looked into the case earlier this week.
Ms Dance says her legal team has been given a “strict timeline” of 9am to file the ECHR application - two hours before the cut-off mark for treatment.
“Every single court case we’ve had we’ve had no time at all, one or two days to prepare and get the whole case together,” she said.
Alistair Chesser, chief medical officer for Barts Health NHS Trust, which runs the London hospital where Archie is, expressed “deepest sympathies” with Archie’s family.
“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,” he added.
Archie’s family have reportedly been maintaining a vigil by his bedside as they prepare for what could be his last moments.
They spent Tuesday night playing his favourite music and TV shows, Ms Carter is reported as saying by the Daily Mail.
The boy, who was a keen martial arts fighter, was also played messages from boxing stars, according to the newspaper.