"Dear Michael. You are always in my prayers," wrote Hamilton. "Prayers of hope that you pull through this difficult time. You have already achieved so much, given so much."
"May God watch over you and show you the way back to your family, fans and friends."
Button’s letter recalled his strongest recollections of the racing driver.
"When I think of Michael Schumacher I think of two things," he wrote.
"The first is of one my earliest memories of being in Formula One driving out of the pitlane in Melbourne and seeing Michael’s red Ferrari ahead of me scattering the leaves as he drove beneath the trees at the approach to turn three. Even in 2000 he was already a legend.
Career in Pictures: Michael Schumacher
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"The second thing I think about it is that familiar red car snaking about in my mirrors. Michael was such a formidable racer relentlessly competitive - Always There.
"He’s fighting his greatest battle right now and I know everyone at Formula One will hope that he will win again. I certainly hope he will."
Car racing legend Niki Lauda also wrote Schumacher a heartfelt letter.
"Michael, every day I follow the news on your progress and every day I am close to you. I hope I will be able to talk to you very, very soon."
Schumacher's wife, Corinna, recently thanked fans for all their support in a letter published in the Grand Prix programme:
"The German Grand Prix gives me the perfect opportunity to cordially thank you for all your good wishes and positive energies you keep sending Michael," she wrote. "I have to say your sympathy blew us all away! Good to know that together we made it through the hardest time!”
Schumacher suffered near-fatal head injuries during a skiing accident in French resort Meribel in December last year. He is currently being treated at Grenoble hospital in Switzerland, near his family house.
New speculation today suggests that he could return home by the end of the month, although he will need constant support.
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