Alarcon said the timing of Castro's return to public life would depend on his recovery and indicated that sceptics were in for a surprise.
Alarcon dismissed as "speculation by gossipmongers" a Spanish newspaper report that Castro had had three failed operations on his large intestine since last July that caused severe infection.
El Pais, citing medical sources close to a Spanish surgeon who examined Castro in December, reported last week that the Cuban leader's prognosis was "very grave" because his surgery ran into complications after he chose a riskier operation to avoid a routine though uncomfortable colostomy.
Castro underwent initial surgery to stop intestinal bleeding caused by working too hard, the government said. Details of his condition are a state secret.
US officials have said they suspect he has terminal cancer.
But El Pais said he had surgery for diverticulitis, pouch-like sacks in the intestine that can become inflamed and infected.
Castro's main ally, Hugo Chavez, the Venezuelan president, said last week that his Cuban mentor was "fighting a battle for life".
On Wednesday, Chavez read a letter from Castro to the media, displaying Castro's signature as evidence that reports he was dying were false.
"We are really pleased, Fidel, with the news that we have received about your recovery," Chavez said.