Bush spokesman Jim McGrath later explained that he circulated a prepared statement expressing Bush's sorrow at the "death" of the former South African president after misreading a Washington Post news alert about Mandela's discharge from hospital.
Mandela, 95, had earlier returned to his Johannesburg home today after spending three months in hospital for a respiratory illness.
"The 41 stmnt sent this morning was the result of my mis-reading the header on the WaPo news flash. Stupid mistake by me. Apologies to all," McGrath wrote on his Twitter account @jgm41. "The mistake was mine and not the Bushes," he added later.
Mandela has faced several health scares in recent years and his lung problems date back to his 27 years in apartheid jail.
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His latest hospitalization has been his longest since he walked free from jail in 1990 and went on to become the country's first leader to be elected in all-race elections.
In June, the beloved leader was said to be on life support but has recently been reported to be breathing on his own.