Prof Jean-Francois Payen described Mr Schumacher's condition as "stable"
Former motor racing champion Michael Schumacher's condition has improved slightly after an operation to relieve pressure on his brain, his doctors say.
They said a scan carried out overnight showed signs that he was "better than yesterday", although he was still "not out of danger".
The seven-time Formula 1 champion suffered head injuries on Sunday in a skiing accident in the French Alps.
The 44-year-old is in a medically induced coma at a hospital in Grenoble.
An initial scan on Monday night showed "an improved situation" and indicated a window of opportunity for a second operation, doctors said.
The family took the "difficult decision" to give consent for the procedure, and doctors operated on Schumacher for about two hours.
Schumacher's skiing accident dominates German media
coverage, with many painting an image of a fearless
daredevil. "The fight of his life," tabloid Bild says in its
front-page headline, adding: "Schumi was always in
search of danger."
Some commentators, such as Stefan Frommann in daily
Die Welt, wonder whether Schumacher's retirement from
Formula 1 in 2012 has led him to live "more dangerously".
But in Frankfurter Allgemeine Zeitung, Anno Hecker says
those who accuse Schumacher of having gambled with his
life "fear the truth - that they don't dare to do what
Schumacher does: take a risk".
Many others, he adds, see "such winners not as gamblers,
but as people who managed to do what they dreamed of:
to get on, to find out their true potential".
A subsequent scan revealed a "slight improvement".
"We can't say he is out of danger but... we have gained a bit of time,'' said Dr Jean-Francois Payen. "The coming hours are crucial.
"All the family is very much aware that his state is still sensitive and anything can happen."
Doctors said it was impossible to give a prognosis for his condition in the coming days and months.
Schumacher had been skiing off-piste with his teenage son when he fell and hit his head.
His manager, Sabine Kehm told reporters that his helmet cracked on impact.
"It looks like probably that initiating a corner, he was hitting a stone which he had not seen and was catapulted down on a rock," Ms Kehm told reporters.
"That does not mean that Michael was travelling at high speed. He was not too fast," she added.
Messages of support have come from around the world.
Michael Schumacher won seven world championships during his career
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, says the BBC's Imogen Foulkes in Grenoble. He is seen as a kind and 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 but 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.