The family issued the statement yesterday, one week after the 87-year-old Nobel literature laureate was released from a Mexico City hospital, where he had stayed for eight days to be treated for lung and urinary tract infections.
The brief statement made no mention of a report earlier in the day by Mexican newspaper El Universal that Garcia Marquez is fighting cancer and is receiving palliative care due to his age.
El Universal, citing "reliable sources," said the cancer had spread to his lungs and liver.
An oxygen tank and a medical bed were taken to his house right before the author of "One Hundred Years of Solitude" left the hospital on April 8.
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"His condition is stable but very fragile and there are risks of complications due to his age," said his wife, Mercedes, and sons Rodrigo and Gonzalo.
The journalist was diagnosed with lymphatic cancer in 1999 but was later declared to be free of the disease.
Garcia Marquez has made fewer and fewer public appearances in recent years.
His last hospitalisation on March 31 was only made public four days later.
His son, Gonzalo Garcia Barcha, told reporters at the time that the family decided to hospitalise him as a precaution and that there was no emergency.
The author's last public outing was on March 6, when he came out of his house to greet journalists who visited him for his birthday.
His brother Jaime said in July 2012 that his famous sibling was suffering from dementia.
The 1982 Nobel laureate is a pioneer of so-called magical realism, writing epic stories of love, family and dictatorship in Latin America.