Crowds of supporters gathered outside the Caracas hospital where he died, chanting “We are all Chavez!”
Following his death, Vice-President Nicolas Maduro will assume the presidency until an election is held within 30 days, Foreign Minister Elias Jaua said.
“It is the mandate that Comandante President Hugo Chavez gave us,” Mr Jaua told state television, adding that Mr Maduro would also be the candidate of the governing United Socialist Party (PSUV).
It was not immediately clear when the election would take place.
Mr Chavez`s illness prevented him from taking the oath of office after he was re-elected for a fourth term in October.
The exact nature of his cancer was never officially disclosed, leading to continuing speculation about his health, and he had not been seen in public for several months.
Seven days of national mourning have been declared and his body will lie in state until a funeral on Friday.
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