Formula One legend Michael Schumacher's condition has shown a slight improvement after a second operation but he is not out of danger, doctors said Tuesday.

"We are surprised by the improvement," one doctor said at a press conference, adding that the medical team had "gained some time". Schumacher has been in a medically-induced coma after a skiing accident in the French Alps on Sunday.

He first received treatment for head injuries after a ski accident at Meribel on Sunday, officials at the French ski resort reported.

The seven time German world champion, who reportedly owns property at the resort, was skiing off-piste with other skiers when he sustained a knock to the head in a fall.

The 44-year-old was hospitalised at the nearby town of Moutiers, officials said, before being taken to hospital in Grenoble.