Felipe Massa is attended to by F1 medical officer Gary Hartstein
Ferrari driver Felipe Massa will be kept under sedation for 48 hours after he suffered a fractured skull during Hungarian Grand Prix qualifying.
The Brazilian hit a tyre wall after a spring from Rubens Barrichello's car flew up and hit his helmet.
Massa was woken on Sunday for a brain scan that produced reassuring results.
"It brought the result that we had expected concerning an injury of this type," said doctor in chief Peter Bazso at Budapest's AEK military hospital.
Massa's father, mother and pregnant wife have flown in to Hungary from Brazil, and the doctor added that the driver remained in intensive care and in an "acute phase" of treatment.
Massa's engineer reflects on crash (UK only)
Ferrari team principal Stefano Domenicali told BBC Radio 5 Live: "The situation is stable and positive but we need to stay calm and give the right time for his body to respond to the situation."
Massa's race engineer Rob Smedley told BBC Sport: "There is hope now which at one point (on Saturday) there wasn't. His injuries seem to be not as bad as we first thought.
"I don't even want to think about F1 at the moment - Felipe is a mate, he is like a little brother to me. I just want to think about him getting better and being back with his family.
"He is still in intensive care and we are all just waiting for news hour by hour. We don't know how long he will be kept in there - it could be days, it could be weeks."
An earlier Ferrari statement said: "After undergoing an operation yesterday afternoon, Felipe Massa's condition remains stable and there were no further complications through the night."
A statement from the hospital on Saturday said: "At the time he was admitted to hospital his condition was stable and he was breathing and blood circulation was normal.
"During the course of his examination they established that he suffered serious, life-threatening injuries including loss of consciousness and a fracture of the forehead on the left side and a fracture on the base of the skull.
"After the operation he is being cared for in intensive care and now he is in stable, satisfactory condition."
I honestly don't believe in coincidences in life. Things happen for a reason and I think this is the second message
Barrichello said on his Twitter feed that he had visited his compatriot Massa in hospital and the surgery "went very well".
The incident comes days after Formula Two driver Henry Surtees, 18, was killed in what was described as a "freak" accident during a race at Brands Hatch.
The son of motorsport legend John Surtees was struck by a wheel which flew off a competitor's car.
After being struck on the head, Massa's feet are believed to have come to rest on both the throttle and brake and his car ploughed head on into a tyre wall at around 125mph.
The 28-year-old was swiftly attended to by trackside medics before being taken to the circuit's medical centre, after which he was airlifted to hospital.
Barrichello later led the calls for more stringent safety measures to be looked into. Referring to Surtees, the veteran Brazilian refused to believe the two incidents were coincidental.
"I honestly don't believe in coincidences in life," he said. "Things happen for a reason and I think this is the second message.
Something broke on my car - Barrichello
"Imola [where Ayrton Senna died in 1994] was a message and the cars were improved. Unfortunately, we lost a boy [Surtees], which is tremendously sad.
"It is not a coincidence something happened right now. In the GPDA (Grand Prix Drivers' Association) we talked quite a lot about it yesterday - and something needs to be done. Absolutely.
"But I don't know what. We need to sit down and have a look at it. I think the cars are a hell of a lot safer, really a lot safer, but there is no coincidence on this and something needs to be looked at."
Lewis Hamilton described the crash as "very scary" and said it must be looked into, while Jenson Button said it proved there "is still more we need to do on safety".
Button and Barrichello's team boss Ross Brawn said the team were "naturally concerned" about Massa's condition.
"We had a problem with the back of the car and we are still investigating," he added.
"We haven't had the piece back from [motorsport governing body] the FIA yet so once we get it back we can understand what occurred.
"It's the first time we've really had a problem with the car as it has been so reliable."
McLaren team boss Martin Whitmarsh added: "What happened today was a shock.
"We've got to make sure we do everything we can to make F1 as safe as it can be.
"But a spring coming off and being in a collision four seconds later is an incredible circumstance and coincidence.
"You have to remember that motor racing is dangerous and that racing drivers are incredibly brave. It's all too easy to become blase about that."