Formula 1 legend Michael Schumacher's condition has improved slightly after a second operation following his life-threatening ski accident, but he's "not out of danger", doctors treating him say.

Surgeons said they had won some time by performing a successful second procedure on the seven-times world champion on Monday night, but his status remained critical.

His wife and two children are at the hospital in the French alpine city of Grenoble, where Schumacher is in a coma after he fell and slammed his head on a rock while skiing off-piste on Sunday.

News of the accident stunned the world and motor racing stars joined German Chancellor Angela Merkel and legions of fans in expressing their hopes for the recovery of the greatest champion in formula one history.

Schumacher, 44, underwent an operation soon after being flown by helicopter to the hospital, and surgeons performed a second nearly two-hour-long procedure on Monday to remove bleeding in the left side of the brain.

Jean-Francois Payen, head of the intensive-care unit, warned at a press conference on Tuesday that Schumacher was not out of the woods.

"We cannot speculate on the future," he said. "We cannot say he is out of danger, but we have gained some time."

He said scans showed that the removal of the bleeding had been done in a "satisfactory manner", but ruled out Schumacher's transfer from the hospital, as it could be "dangerous".

Doctors have said Schumacher, who is due to turn 45 on January 3, has age and physical fitness on his side.

He had been put in a medically induced coma to spur recovery. His temperature has also been reduced to about 35 degrees to reduce swelling.

By being unconscious, the brain is also switched off to sounds, light and other triggers that cause the organ to use up oxygen as it processes the stimuli.

A source close to an investigation into the off-piste accident at the upmarket ski resort of Meribel said Schumacher's helmet, which medics say saved his life, was smashed "in two" by the impact.

Schumacher was skiing with his 14-year-old son when he fell and crashed into a rock. His son was unhurt.

The German newspaper Bild also quoted a rescuer as saying the split helmet was "full of blood".

Schumacher's family remained "worried", despite the slight improvement, his manager, Sabine Kehm, said.

Several people had tried to sneak through the hospital and approach the former racer, she said, asking that he and his family be left in peace.

"There apparently was a person dressed up as a priest, who tried to get near Michael. I am asking everyone to let the doctors work and leave the family to spend peaceful time with Michael," she said, as messages of support poured in. AFP