(CNN) -- Michael Schumacher, the most successful driver in Formula 1 history and one of the world's highest-profile athletes, remains in critical condition after suffering severe head trauma in a skiing accident in the French Alps, hospital officials said Monday.
Doctors who have been treating Schumacher at the University Hospital Center of Grenoble said at a news conference that it was too early to say what the driver's prognosis might be.
In a prepared statement, Schumacher's family thanked doctors for doing "everything possible to help Michael." They also thanked people around the world for the outpouring of support.
The German, who retired from the elite motorsport for the second time in 2012, fell and hit his head on a rock Sunday, said the director of the Meribel resort where Schumacher was skiing.
Schumacher was in a coma when he arrived at the hospital and required immediate brain surgery, officials said. So far, he has undergone one operation and is being kept in a coma, they said Monday.
Schumacher, who turns 45 Friday, won a record seven world titles in his spectacular Formula 1 career and "also holds nearly every scoring record in the book by a considerable margin," according to the motorsport's official website.
He dominated the competition for the best part of a decade, winning five world championships in a row between 2000 and 2004.
Schumacher suffered serious injury once during his career in the high-speed sport, breaking his leg in a crash at the British Grand Prix in 1999.
Wearing a helmet
His skiing accident happened while he was off-piste (on unmarked slopes) Sunday morning in the mountains between Georges Bauduis Piste and La Biche Piste, resort director Christophe Gernignon-Lecomte said.
Schumacher was wearing a helmet when he hit his head, Gernignon-Lecomte said. Rescuers reached him minutes later, and he was airlifted to a nearby hospital, the director said.
Doctors at the Grenoble hospital said that without the helmet's protection, Schumacher wouldn't have made it to the operating table.
The cause of the accident, which is being investigated by police, remains unclear, Gernignon-Lecomte said.
Schumacher "was not alone" when he fell, his spokeswoman Sabine Kehm said in a prepared statement. But nobody else was involved, she said.
'A great champion'
Former French Formula 1 driver Olivier Panis visited the hospital in Grenoble on Sunday but was not able to see Schumacher, CNN affiliate BFM TV reported.
"As I am here in Grenoble, I want to come to him and say hello, for old times' sake. He is a great champion and someone very loved in Formula 1," Panis told BFM.
Schumacher has a wife, Corinna, and two children, Gina-Maria and Mick. His brother Ralf was also a Formula 1 driver.
Schumacher made his Formula 1 debut in 1991 and won a record seven world titles -- five of them with Ferrari -- by the time he retired for the first time at the end of the 2006 championship.
In that period of temporary retirement, he was involved in a motorcycle crash in Spain in 2009 that left him with a lingering neck injury, which delayed his racing comeback.
He returned to the Formula 1 track with the revived Mercedes team in 2010 but struggled to repeat his earlier glories.
His best finish was third place at last year's European Grand Prix in Valencia, his only podium position in three seasons with the German manufacturer.
'A very good skier'
Sunday's accident occurred at a popular ski resort in an area known for its challenging slopes above the tree line.
"If you are anything less than a really experienced skier, it's very easy to lose your bearings, because you don't see much in the way of vegetation around you or anything else," said Paul Hochman, a former contributing editor at SKI Magazine. "It's just literally all white, all snow."
British journalist Kevin Garside told CNN that Schumacher is "a very good skier" but acknowledged that he is "fearless" -- like most Formula 1 drivers.
"These people don't recognize fear like you and I do. There is no gene in their body that lets them go slow," Garside said.
"Schumacher wasn't a skier when he joined Ferrari (in 1996), but by the end he was excellent," he said. "Each year Ferrari used to have a media week in the Alps in Italy and they would always have a race -- and it was always Schumacher who won. He was a genuinely quick skier.
"But he was always very mindful of the danger around him," Garside added. "I approached him for an interview at the top of the slope, and he said it would have to be quick as he wanted to check the piste. That meant he wanted to make sure he understood the slopes, the cambers, even though it was only a fun race."
CNN's Elwyn Lopez, Jonathan Mann and Christina Macfarlane contributed to this report.