Michael Schumacher's family in bedside vigil after ski accident

Schumacher's manager, Sabine Kehm, said his wife, Corinna, daughter Gina Maria and son Mick are in a state of shock at the Grenoble hospital.

The seven-time Formula 1 champion suffered head injuries on Sunday in a fall at the resort of Meribel.

He has been put in a medically-induced coma to relieve pressure on his brain.

"The family is not doing very well, obviously. They are shocked," Sabine Kehm told reporters.

Prof Jean-Francois Payen, of Grenoble University Hospital's intensive care unit, told a news conference that they could not give a prognosis for the 44-year-old driver.

"He is in a critical state in terms of cerebral resuscitation. We are working hour by hour," he said.

Prof Payen said that if Schumacher had not been wearing a helmet "he wouldn't be here now".

"We had to operate urgently to release some pressure in his head," the anaesthetist said.

Neurosurgeon Stephan Chabardes said that a post-operative scan had shown "diffuse haemorrhagic lesions" on both sides of Schumacher's brain.

Schumacher is likely to stay in an induced coma for at least 48 hours, or even several weeks, she adds - and there can be many months of therapy in order to achieve as full a recovery as possible.

Doctors have lowered Schumacher's body temperature to 34-35C (93.2-95F) as part of the coma, slowing his metabolism to help reduce inflammation.

The driver had been skiing off-piste with his teenage son when he fell and hit his head on a rock.

He was first evacuated to a hospital in the nearby town of Moutiers.

Prof Chabardes said the driver was in an "agitated condition" on arrival in Moutiers and his neurological condition "deteriorated rapidly".

He was taken from Moutiers to the larger facility in Grenoble.

Messages of support have come from around the world.

A spokesman for German Chancellor Angela Merkel 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.

Former Ferrari teammate Felipe Massa, who recovered from life-threatening head injuries he suffered at the 2009 Hungarian Grand Prix, wrote on Instagram: "I am praying for you my brother! I hope you have a quick recovery! God bless you, Michael."

On Monday some fans had gathered outside the hospital in Grenoble.

Nuravil Raimbekov, a student from Kyrgyzstan who is studying nearby, described Schumacher as an inspiration.

"I'm worried, of course... but I still hope, and I will pray for him," he said.

Schumacher is held in a great deal of affection in the area, our correspondent says. He is seen as a kind a generous man who has done a lot for charity.

The former champion, who turns 45 on 3 January, retired from F1 for a second time in 2012. He won seven world championships and secured 91 race victories during his 19-year career.

The driver won two titles with Benetton, in 1994 and 1995, before switching to Ferrari in 1996 and going on to win five straight titles from 2000.

He retired in 2006, and was seriously hurt in a motorcycling accident in Spain three years later, during which he suffered neck and spine injuries.

Schumacher managed to recover and made a comeback in F1 with Mercedes in 2010. After three seasons which yielded just one podium finish, he quit the sport at the end of last year.