US President Barack Obama led the international condolences, while urging the southern African nation to conduct "a peaceful constitutional transition of power as the country moves forward during this time of sorrow".
Even though officials had long denied he was sick, Sata, 77, died on Tuesday while undergoing treatment in London's private King Edward VII hospital for an unspecified illness, the Zambian government reported.
Sata, nicknamed "King Cobra" for his sharp rhetoric, died only days after Zambia celebrated half a century of independence.
Officials had long denied Sata was sick, even prosecuting journalists who questioned his long "working vacations" to Israel and elsewhere.
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Some Zambians responded to the news by asking why he died in an upscale foreign hospital and expressed anger over government secrecy, including claims he was going to London for a check-up.
"They were cheating," said Mundia Akapelwa, a young mother visiting Lusaka's Soweto market.
"They knew well that he was going to seek medical attention. You can hide sickness but you can't hide death. Now the whole world knows that the man has died in hospital.