Machel issued a statement via the Nelson Mandela Centre for Memory on Monday morning, as Mandela entered his tenth day in a Pretoria hospital, where he is being treated for a lung infection.
"Madiba once said, 'What counts in life is not the mere fact that we have lived. It is what difference we have made in the lives of others.' I have thought of his words on each occasion the world stood with him, making a difference to him, in his healing," Machel said.
She said the outpouring of affection and support had come from South Africans, Africans and from across the globe, in the form of emails, letters, social media networks and "the human voice".
" … In particular, the voices of children in schools or singing outside our home. We have felt the closeness of the world and the meaning of strength and peace.
"Our gratitude is difficult to express. But the love and peace we feel give yet more life to the simple, 'Thank you!'," Machel said.
The former statesman's wife did not provide insight into Mandela's health. However President Jacob Zuma told a Youth Day celebration on Sunday in Newcastle, KwaZulu-Natal, that Mandela's health has shown improvement despite his still being in a serious condition.
"We are grateful that he continues to get better. Over the last two days, although [his condition] remains serious, his doctors have stated that his improvement has been sustained," Zuma said. The president, accompanied by African National Congress treasurer general Zweli Mkhize, visited Mandela on Thursday.
Security remains tight
Meanwhile, well-wishers left flags, flowers, balloons and get-well-soon cards at the entrance to the Pretoria hospital where Mandela was spending his tenth day on Monday.
Colourful messages were printed on large pieces of paper and cardboard attached to the hospital's wall next to the security checkpoint.
Some of the messages read: "Get well soon from the sickness. Long live. From Lazarus [in] Atteridgeville". Another read: "I love you Tata Mandela. From Sharon Duduza". Two flags were tied onto the hospital's security wall along Celliers Street. A message on one of the flags read: "The long walk to freedom continues".
Several multicoloured balloons, were also swinging next to the flags and bouquets of flowers lined the sidewalk. Passers-by briefly stopped at the entrance to the hospital and read the messages of support.
Mandela (94) was hospitalised in the early hours of June 8 with a recurring lung infection.
Security at the Mediclinic Heart Hospital remained tight. On Monday morning, several police officers were searching all vehicles entering the hospital's two entrances. A contingent of local and international media continued to monitor the entrances.
Members of the Mandela family visited the ailing icon on Father's Day.
Mandela's former wife and ANC MP Winnie Madikizela-Mandela, daughter Zenani Mandela-Dlamini and Mandela's granddaughter Zaziwe were at the hospital on Sunday. – Additional reporting from Sapa