Preston Flores remains in a critical condition in hospital after suffering burns over much of his body when petrol was allegedly taken from a vehicle near where he was playing with his cousins in Aberdeen.
His mother Luisza said: "We are very grateful for everything that has been done to help Preston and his family at this extremely difficult time."
She added: "On behalf of us all I want to thank the medical staff and the emergency services for all they are doing to help us.
"We are also very appreciative of the support of our friends and the local Bedford community as well as the wider public. We thank everyone for their help in our time of need and would kindly request that we are now allowed our privacy to deal with this as a family ourselves."
The emergency services were called to Bedford Avenue just before 2pm on Friday afternoon and Preston was taken to hospital by an ambulance escorted by police vehicles.
He was later transferred by air ambulance to a specialist burns unit at the Royal Hospital for Sick Children in Edinburgh.
Concerned locals told how youngsters were seen apparently handling a fuel can before the incident.
Police said information from local residents that the incident may have involved petrol from a council van was "forming part of the investigation".
Paulina Pilska, 25, said she watched Preston running from the side of a building with flames all over one side of his body.
The cleaner said: "I was watching from my window and could see three boys and one girl jump on top of a council pick-up van.
"They were searching for something. I saw one of them with a container, like a watering can.
"A few moments later the boys ran off. Then I saw a boy with fire on him coming from the lane."