Former Formula 1 champion Michael Schumacher's condition has improved slightly after a second surgery to relieve pressure on his brain, French doctors have said.

A new scan taken overnight showed signs that he was "better than yesterday", but he was still "not out of danger", doctors, cited by the BBC, explained Tuesday.

Schumacher, a 7-time Formula 1 champion, was skiing off-piste with his teenage son, when he fell and hit his head on a rock. He was transferred to a hospital in Grenoble after the skiing accident in the Alps resort of Meribel, with a serious head injury.

Prof. Jean-Francois Payen told reporters that if Schumacher had not been wearing a protective helmet, "he wouldn't be here now".

Doctors placed him under induced coma to try to stabilize the pressure within the brain and to prevent secondary brain damage from occurring.

His family, which is on a vigil at the hospital, has taken the "difficult decision" to give consent for the second procedure, and doctors operated on Schumacher for about two hours.

A follow-up scan revealed a "slight improvement".

"We can't say he is out of danger but... we have gained a bit of time. The coming hours are crucial. All the family is very much aware that his state is still sensitive and anything can happen," Payen explained Tuesday.

Doctors said it was impossible to give a prognosis for his condition for tomorrow, six months' or even a year's time.

Four years ago, Schumacher suffered a spinal injury when falling off a motorbike. During his car racing career, he also had several accidents, but with minor injuries.

Messages of support keep pouring in from around the world.

A spokesman for German Chancellor Angela Merkel, cited by the BBC, said she and her government were, like millions of Germans, "extremely shocked".

"We hope, with Michael Schumacher and with his family, that he can overcome and recover from his injuries," the spokesman said.