The parents of the boy “thrown” from the Tate Modern have said they still do not know the full extent of his injuries.
The six-year-old boy was on holiday with his family, who are from France, when he fell five storeys from the art gallery’s 10th-floor viewing platform.
A court hearing was told the boy suffered a bleed on the brain and fractures to his spine, arms and legs.
He was initially in a critical condition following the incident on 4 August, and has so far undergone “two long and difficult operations”.
In a message posted on a fundraising page, the boy’s parents said his condition has stabilised.
“We still do not know the full extent and severity of his injuries,” they added.
“But he is alive, struggling with all his strength and we remain hopeful.”
More than €51,000 (£46,600) has so far been donated to a crowdfunding page by more than 1,300 people.
The parents thanked people for their donations and messages of support, adding: “You cannot imagine how it helps us to see so much humanity in this tragic ordeal. Thank you very much; you help us to keep going.”
London nurse Vicky Diplacto, whose brother was paralysed in a similar incident overseas, said she set up the GoFundMe appeal “in order that he [the boy] may receive gold-standard care and support”.
A 17-year-old boy has been charged with attempted murder and is to undergo a psychiatric assessment before standing trial next year.
A court heard that the six-year-old had been at the Tate Modern with his parents, on the viewing platform “looking over the side and enjoying the view”.
The child is said to have walked a short distance from his parents and was allegedly picked up and thrown over the edge in an action that was “carried out extremely swiftly and in one movement”, the court heard.
The suspect was apprehended by members of the public after the incident.
A reporting restriction bans the identities of both the victim and the defendant being made public.