Formula One legend Michael Schumacher showed a "very slight" improvement after a second operation Tuesday on a critical head injury sustained in a skiing accident Sunday.

Messages of sympathy and support continued to flood in for the comatose seven-time F1 champion, who won five of those titles with Italian team Ferrari.

Former US president Bill Clinton said he was praying for Schumacher, who donated millions of dollars to Clinton's philanthropic foundation among the huge sums he gave to charity during the latter stages of his career.

Clinton tweeted: "Thinking today of Michael Schumacher and grateful for all he's done w/@clintonfdn and for others. My prayers are with him and his family".

Three-time former F1 champ Niki Lauda also said he was praying for his stricken Ferrari predecessor.

The Austrian, who survived a horrific fireball crash at the Nuerburgring in 1976 that left him badly scarred, said of the great German: "I pray to God that it will all end well but sadly it doesn't seem that way at the moment".

Lauda, 64, won the F1 title for Ferrari in 1975 and 1977 and for McLaren in 1984.

Schumacher, who turns 45 on Friday, won five straight titles for Ferrari from 2000 to 2004 after triumphing with Benetton in 1994 and 1995.

He is the most successful F1 driver ever, with 91 grands prix and a string of records for race times, pole positions and podium finishes.

The Italian press was full of messages from drivers and admirers Tuesday.

Four-time and reigning F1 champ Sebastian Vettel said of his countryman: "He's like a father for me, I can't lose him.

"It's the most important grand prix of your life, you have to win".

Two-time F1 champ and current Ferrari ace Fernando Alonso said: "Michael, you're a strong man, get well soon".

Echoing a Ferrari message Monday, Alonso added: "I hope to hear positive news soon".

MotoGP great Valentino Rossi said on his Twitter feed: "Come on Schumi, don't give in, you've never done that.

We're all with you".

Former Napoli and Argentina soccer great Diego Maradona said: "You're a guy who's full of life, an example as driver and man. Come on my friend, you'll do it one more time".

Doctors working to save Schumacher said it was too early to say he was "out of danger". "It's too early to say what will happen, impossible to make predictions. It would be stupid to talk about it," they told a press conference at a Grenoble hospital.

"The patient remains fragile, the next few hours will be crucial.

"For now he is staying here, where he has the best treatment possible.

"Then we will decide whether moving him to Germany is possible".

Schumacher flipped on a stone and banged his head on a rock while skiing with his son in the French Alps Sunday and, after initially seeming OK, was put into a drug-induced coma after collapsing with a brain haemorrhage. Schumacher's personal doctor and friend, Gerard Saillant, said the fight to save the ex-driver was tough but he was more optimistic after the second operation.

"The battle remains difficult, although now there is a little bit more optimism," Saillant told the press conference at the Grenoble hospital Schumacher was rushed to after the accident near Meribel.

"For now it is impossible to make predictions about the clinical future of Michael Schumacher, it's stupid even to talk about it," said Saillant.

Schumacher had a part of his skull removed Sunday to ease pressure on his brain and another operation early Tuesday to remove a large haematoma on the left side of his brain.