Farinas began his hunger strike after the death on February 23 of Orlando Zapata Tamayo, a jailed dissident who refused to eat for 85 days to protest prison conditions.
Zapata, who had been imprisoned since 2003 on charges including disrespecting authority, was the first imprisoned opposition figure to die after a hunger strike in Cuba in nearly four decades.
Farinas, who has conducted 22 previous hunger strikes, has been in a hospital in the central city of Santa Clara receiving fluids intravenously since he collapsed on March 11.
The government has asked him to drop his hunger strike because of his frail health, but he has said he is ready to die for his cause.
"Everything possible is being done to save his life, but if he does not change his self-destructive attitude, he will be responsible, together with his backers, for the outcome we don't want," Castro said.
"The Cuban government doesn't care about the life of Farinas"
Licete Zamora, a spokeswoman for Guillermo Farinas
The Cuban leader noted that Farinas is not behind bars, saying "he is a free person who has already served his sentence for common crimes".
But Licete Zamora, a spokeswoman for Farinas, said that Cuba's leaders would be to blame if Farinas dies.
"The Cuban government doesn't care about the life of Farinas," she told the Reuters news agency from Santa Clara.
"If they don't give him a satisfactory response, the world can't be accused, they have to be accused."
Havana insists it keeps no political prisoners, branding the dissidents in jail as "mercenaries" in the pay of Washington.
Hillary Clinton, the US secretary of state, and the European Parliament have condemned Cuba for Zapata's death, and a group of artists and intellectuals including Spanish film director Pedro Almodovar have circulated a petition criticising the Cuban government.
Amnesty International lists Cuba as holding 55 so-called prisoners of conscience in its jails.