The 81-year-old "Sinatra of Rancheras" continued to depend on a ventilator to help him breathe, the statement said, and his brain function was described as normal.
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"We expect forward progress in his recovery," the Spanish-language post said. "His post-operative care will require immediate physical and pulmonary rehabilitation."
The beloved singer suffered a fall at his ranch Los Tres Potrillos, located outside the city of Guadalajara, resulting in a spinal-cord injured, according to a previous statement from this family.
In recent years, Fernández has been afflicted with multiple health conditions. He was recently hospitalized with a kidney infection, and in 2012 he he underwent a complex surgery in which almost half of his liver was removed due to a tumor. A year later, he faced a pulmonary thrombosis.
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In March 2015, three hernias that had formed during the recovery process from the liver operation were removed.
The Associated Press contributed to this report.