The family of Michael Schumacher described the Formula One legend as a fighter who "will not give up", as he turned 45 on Friday while lying comatose in a French hospital.

"Following Michael's skiing accident, we would like to thank the people from all around the world who have expressed their sympathy and sent their best wishes for his recovery," the Schumacher family said in a statement posted on the German racing great's website.

"We all know he is a fighter who will not give up" they added, in the message coinciding with his birthday.

Doctors and family members were tight-lipped on Thursday about the condition of the retired Formula One champion who has been hospitalized since Sunday, when he slammed his head against a rock while skiing in the French Alps.

There have been conflicting statements about the speed the seven-time world champion was going when he crashed at the Meribel ski resort, where he has a property.

The impact split the helmet Schumacher was wearing in two, according to a source close to the investigation.

The Ferrari F1 team, where Schumacher spent many years, announced it would hold a "silent gathering" on Friday in front of the Grenoble hospital where he is being treated to mark the birthday of the ex-driver, who is being kept in an induced coma.

But Schumacher's fan club in his childhood town of Kerpen said any celebration of his birthday would be in bad taste.

The hospital and Schumacher's manager had briefed the press daily since the accident, but they did not do so on Thursday, instead promising to communicate only if there was something new to report.

Schumacher has had two operations to remove bleeding and pressure on his brain. His media representative, Sabine Kehm, said on Wednesday that Schumacher's condition was stable but still critical.

Prosecutors have opened a probe into the accident, as is common practice in France in such cases, and are exploring the theory that Schumacher was skiing at great speed when he fell. That factor could help establish liability or negligence, depending on circumstances.

The prosecutors are also looking at whether the limits of the courses next to the area where accident happened were correctly marked and whether the safety releases on Schumacher's skis operated properly.

The German newspaper Bild reported the skis were rented and one of their safety releases did not open at the moment of the accident.

Prosecutors were not expected to make any statement on the investigation until early next week.

The hospital has been faced with intense media pressure from the worldwide interest in its famous patient. A vacant lot nearby has been turned into an impromptu parking lot for numerous TV satellite vans.

Kehm earlier in the week said some people had tried to sneak into Schumacher's room, one dressed as a priest.

The three medical professors treating him - two neurosurgeons and the head of the anesthetic and intensive care department - have also been thrown into the spotlight.

They have appeared at the two press conferences to explain the latest developments. While they have refused to speculate on how Schumacher's condition might evolve, they agree that his age and fitness could help with recovery.

Schumacher, who made his F1 debut in 1991, dominated the sport, winning more world titles and races than any other driver.

He first retired at 37 but was unable to resist the lure of the track. In 2010 he came out of retirement but could not recover his previous levels of performance and quit for good in 2012.

As an F1 racer, Schumacher was known for his daring overtaking manoeuvres, an almost reckless abandon in the pursuit of victory and his mastery of tricky conditions presented by rain.