Fidel Castro is said to be making a good recovery since illness forced the 79-year-old Cuban leader to hand over power to his brother Raul temporarily.
The Venezuelan government, currently Cuba's closest ally, said it had been told Mr Castro's recovery was "progressing positively".
It is not clear whether he is in hospital or recovering at home.
He has had surgery to halt internal bleeding, according to a statement attributed to Mr Castro himself.
The Cuban leader, who turns 80 this month, was quoted as saying that a punishing schedule in recent weeks had affected his health.
This is the first time Mr Castro has relinquished any of his duties as head of the communist state since he came to power in 1959.
Stephen Gibbs, BBC correspondent in Havana, says most Cubans are taking news of their leader's sickness in their stride.
Shops and offices are open, and there is no sign of extra security.
The White House has said it is monitoring events while Cuban exiles have been celebrating in Miami.
Raul Castro, the defence minister, has long been designated as his brother's successor should he become incapacitated.
In his statement, Fidel Castro said a recent trip to Argentina and last week's anniversary of the Cuban Revolution had caused him "days and nights of non-stop work" and put him under "extreme stress".
Resulting intestinal bleeding, he said, meant he needed an operation which would require several weeks of rest.
"Since our country is threatened by the US Government under circumstances such as these," the statement said, Mr Castro had delegated his functions as president and first secretary of the Communist Party to his brother Raul, who is 75.
A major celebration had been planned for 13 August - the veteran leader's 80th birthday - but the event has now been postponed until December.
Fidel Castro has been among the world's longest-ruling leaders - outlasting nine US presidents.
The news prompted scenes of wild celebration on the streets of Miami on Monday night, as thousands of people danced, banged cooking pots and chanted "Cuba, Cuba, Cuba!"
"There has never been anything that has given the people so much hope," Armando Tellez, 33, told the Associated Press news agency.
Others, like Miguel Saavedra, the leader of a conservative Cuban exile group, speculated that Mr Castro had already died.
"Castro is dead ... why is he dead? Because the government they give a lot of information to the whole world that Castro passed his power to the brother ... this news now is the best news... for 48 years," Mr Saavedra said.
But others were more circumspect, noting that Mr Castro had survived several health scares.
In 2001, he fainted briefly during a speech.
And in 2004, TV cameras captured the moment when Mr Castro slipped and fell, breaking his knee and fracturing his arm.
The White House said it was monitoring the situation, but did not wish to speculate on Mr Castro's health.
"We will continue to work for the day of Cuba's freedom," said spokesman Peter Watkins.