(CNN) -- The family of former South African leader Nelson Mandela is overwhelmed with support as the 94-year-old remains hospitalized in serious condition.
"So much love and generosity from South Africans, Africans across the continent, and thousands more from across the world, have come our way to lighten the burden of anxiety; bringing us love, comfort and hope," former first lady Graca Machel said in a statement Monday.
She said well-wishers have sent messages via e-mail, social media, cards and flowers. Some sang for the family outside the Mandela home.
"We have felt the closeness of the world and the deepest meaning of strength and peace," Machel said.
Mandela has been in serious condition since he was rushed to a Pretoria hospital June 8 with a recurring lung infection.
On Sunday, President Jacob Zuma said Mandela's health has shown improvement despite his still being in a serious condition, the South African Press Association reported.
Mandela has been in and out of hospitals in recent years. His history of lung problems dates back to when he was a political prisoner on Robben Island during the apartheid era, and he has battled respiratory infections over the years.
He has not appeared in public since South Africa hosted the World Cup in 2010.
Last year, he spent the Christmas holidays undergoing treatment for a lung infection and gallstones, one of his longest hospital stays since his release from prison in 1990.