Raul said on Sunday that he and other leaders held a long meeting with his brother during the last two days at which they discussed "affairs of state" and that Castro gave various instructions.
"Fidel is doing well. He has a telephone and is using it more and more," Raul Castro told a congress of high school students in Havana.
"He is not dying as some press in Miami report, but constantly improving. But as he himself has said it will take time," Raul said.
Time magazine reported at the weekend that US government officials believe Castro, 80, has terminal cancer.
The report was picked up around the world and by the Miami media, where close to a million Cubans live.
The secrecy surrounding the Cuban president's condition and whereabouts has led to constant rumours about what ails Castro, in power for 47 years.
Castro issued a communique on July 31 stating he was temporarily ceding power to his younger brother Raul, 75, because he was undergoing surgery for intestinal bleeding and would need weeks to recover.
Since then state-run media have carried videos and pictures of Castro meeting friends and dignitaries in his hospital room.
The last time being more than two weeks ago when he met Kofi Annan, the UN secretary general in Havana for a non-aligned movement summit.