His brother Joachin told Santiago newspaper Las Ultimas Noticias that he would have another tomorrow and once he recovered from that, he would travel home.
Benjamin was having problems with his shoulder and had a broken collarbone, his brother said.
Joachin Blake said he spoke every day to Benjamin, who is being supported in NZ by their father, Eric, and Benjamin's girlfriend, Macarena.
Joachin Blake said they hoped to return home to Chile next month.
Benjamin wrote about the crash from his hospital bed. He said he and the Argentines had been grateful they were able to experience and enjoy the "great peace" of National Park.
"Every day we went to work in the Whakapapa ski centre. We were meeting people from around the world. We all, I believe, were trying to enjoy every day as much as possible," he wrote.
Benjamin Blake and Macarena lived with Mr Donofrio, his girlfriend Valeria and Mr Caceres, who was known by the nickname "el Chino".
Mr Blake said he looked forward to getting home, but would never forget what the doctors and other clinical staff had done for him.