According to a statement from the leader read on Cuban television Castro is in stable condition and in good spirits.
In the first public statement since he announced late Monday that his brother Raul would take over as president temporarily Castro, who turns 80 on August 13, said he needed time to recover.
"I can say the situation is stable, but a general recovery in health requires time," the statement said.
"All I can say is that the situation will remain stable for several days before a verdict can be reached."
"I am in perfectly good spirits, and the important thing is that everything in the country function and function perfectly well," it said.
President Castro temporarily handed over power for the first time to his brother Raul before undergoing the operation from which he could take weeks to recover.
Raul Castro has maintained a low profile and is still to make his first public appearance as the temporary president.
Cuban dissidents were not surprised by Raul Castro's designation as temporary leader, as he has already been named his brother's heir.
Despite the regime's harrassment of dissidents, opposition leaders wished Fidel Castro well as he recuperates.
"We have not wished for his death, even in the worst moments," said Laura Pollan a leader of the Ladies in White whose husbands have been jailed by the regime.
The leader of Cuba's parliament, Ricardo Alarcon, insisted Tuesday that Castro would "fight until the end."
Mr Alarcon, cited by Cuba's Prensa Latina agency, said Castro had given instructions to top officials to follow before he started resting.
US watching developments
Meanwhile the United States kept a close eye on developments in Cuba but reacted cautiously to the news.
"We don't know what the condition of Fidel Castro is. We don't know the exact facts of this because Cuba is a closed society," said White House spokesman Tony Snow earlier.
Mr Snow added that there was "no reason to believe that" Fidel was dead and also indicated that Washington's policy of trying to isolate Havana was unchanged
He said that the United States had no plans to reach out to Fidel’s brother Raul Castro and still hoped that Cuba would become a democracy.
The US has been the Castro regime's archrival to the north since he took power in 1959.
"The one thing we want to do is to continue to assure the people of Cuba that we stand ready to help," said President George W. Bush's spokesman, who looked ahead to "the day in which they no longer live under the boot of tyranny."
Castro predicted he would be out for "several weeks of rest" following an operation to stem intestinal bleeding.
Exiles celebrate
News that he had relinquished power sparked celebrations among Cuban exiles in Miami who have been waiting decades for Castro’s demise.
Thousands took to the streets of the Florida city shortly after Castro's announcement that he would be going into hospital and briefly relinquishing power.
There are more than a million Cuban-Americans, thousands of whom personally fled communist rule over the course of four decades, most settling in Florida.
The crowd there banged pots and pans, honked car horns, waved Cuban flags and chanted "Viva Cuba Libre" -- "Long Live Free Cuba."
Some rushed to contact friends and relatives in Cuba, the Caribbean's most populous island nation and home to more than 11 million people, by mobile phone.
Raul takes over
Castro has been a major world figure since his band of bearded guerrillas seized power from dictator Fulgencio Batista in January 1959.
His rule has been marked by momentous events such as the Cuban missile crisis, which brought the region to the brink of nuclear war, and the failed US-backed Bay of Pigs invasion in the 1960s.
Castro blamed his ailment on the intense agenda of recent trips to Argentina and eastern Cuba.
"Working day and night and barely sleeping has taken a toll on my health, which has withstood everything (but now) has undergone extreme stress and failed," he said in a statement read by his personal secretary, Carlos Valenciaga.
"That touched off an acute intestinal distress with sustained bleeding, which forced me to undergo delicate surgery," he said.
The operations will "force me to forgo my responsibilities and duties for a few weeks," the statement said.
He said Raul Castro would take over as first secretary of the Central Committee of the Communist Party, commander in chief and president of the government.
Castro also asked that his birthday celebration be postponed to December 2, the 50th anniversary of his landing in southeastern Cuba and the start of his armed campaign in the rugged Sierra Maestra mountains.
Raul Castro, often described as less charismatic than his brother, recently hinted that a collective government might succeed Castro.
During a two-and-a-half-hour speech in Bayamo last week, Castro himself joked that he did not plan to be leading Cuba if and when he hits the 100-year mark.
Speculation about Castro's health peaked after a fall in 2004, when he injured his right arm and left knee. Last November, the Cuban leader, who now exercises every day, said he had recovered from these injuries.