Formula 2 driver Juan Manuel Correa - injured in the accident that killed French driver Anthoine Hubert - remains in intensive care in an induced coma.
Correa, 20, suffered a spinal injury and broken legs in the crash at Spa, in Belgium, on 31 August.
His leg injuries "remain an important concern" and he will undergo surgery when his lungs are "strong enough".
Correa's lungs have "gradually recovered" but his respiratory functions are still being assisted.
The Ecuador-born American is in a London hospital and suffered complications following the crash.
Correa had a four-hour operation in Liege, but on arrival in London was diagnosed with acute respiratory distress syndrome.
"Juan Manuel remains in the Intensive Care Unit in a state of induced coma," his management company Race Tech Development Group said in a statement.
"Although his lungs have gradually recovered, his respiratory functions continue to be assisted by ECMO [extracorporeal membrane oxygenation] and a breathing ventilator.
"Juan Manuel's leg injuries remain an important concern and will undergo immediate surgery once his lungs are strong enough to withstand the procedure."
Hubert, who was 22, suffered a huge impact from Correa's car, which was travelling at about 170mph, at the Spa-Francorchamps circuit.
The Frenchman was taken to the medical centre following the incident, and died shortly after.
Correa, who grew up in Miami and lives in Barcelona, has been racing this season with the Sauber junior team and is the development driver for Alfa Romeo Racing's F1 team.