Michael Schumacher’s family has described the Formula One champion as a “fighter” in a message thanking fans for their support following his skiing accident.

The racing driver, who suffered a severe head injury while skiing off-piste in the resort of Meribel in France last Sunday, remains in an induced coma in hospital.

He is in a critical but stable condition and it is believed that his life was saved by his skiing helmet, which split on impact.

In a message posted on Schumacher’s website, his family wrote: “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. They are giving us great support.

“We all know he is a fighter and will not give up. Thank you.”

After the accident, which happened while Schumacher was skiing with his family, rescuers were on hand within minutes. The driver, who turns 45 on Friday, was initially conscious before deteriorating into a critical condition.

He was airlifted to Grenoble hospital, where neurosurgeons have operated twice to remove blood clots on the brain and reduce swelling.

Doctors have said the impact caused numerous brain injuries including intracranial haematomas (multiple blood clots), bilateral lesions and bruising of the brain.

An initial operation carried out on Sunday to reduce swelling was followed by a second to remove the largest of a number of clots in his brain. Jacqueline Hubert, the Grenoble hospital’s director general, said on Tuesday that his condition had started to improve.

Schumacher retired from F1 for the final time in 2012 after a three-season comeback with Mercedes. Schumacher, who also raced for Jordan, Benetton and Ferrari, won the last of his world titles in 2004.

He won two with Benetton in 1994 and 1995 before moving to Ferrari and winning five in a row from 2000. The German had 91 career wins.

Ferrari announced they would organise a gathering outside the Grenoble hospital on Friday to mark his birthday.