Archie Battersbee, 12, was found unconscious three months ago.
Doctors treating him at the Royal London Hospital say continued treatment should end.
Archie’s parents Hollie Dance and Paul Battersbee, from Southend, disagree.
A judge who reviewed evidence at the Family Division of the High Court concluded yesterday that ending treatment was in Archie’s best interests.
Ms Dance said she now wanted to ask Court of Appeal judges to overturn the ruling.
She said: “With all due respect, it is not in Archie’s best interests to die. Archie would want us to keep on fighting. And we will keep on fighting. We will appeal.”
“As long as Archie is fighting for his life, I cannot betray him.”
“Until Archie gives up, I won’t give up. We will be appealing this ruling and we ask for your prayers and support.”
“I am living every parent’s worst nightmare.”