"Reports that the president is in a coma and that the family is discussing ending life support, are totally false," Adan Chavez, governor of the state of Barinas, said in a statement.
He "continues to respond well to his medical care and to make daily progress in his recovery."
Chavez, whose OPEC-member nation controls the world's largest proven oil reserves, has been out of public sight since undergoing surgery in Havana on December 11, the fourth such operation in the 18 months since his condition was made public.
Previously, officials said the fiery leftist leader was suffering from a severe pulmonary infection that resulted in a "respiratory insufficiency," fueling speculation about his prospects for a full recovery -- and his political future.
The uncertainty surrounding Chavez's condition has rattled Venezuela.
The government was forced to postpone the president's scheduled inauguration Thursday, as it became clear that he could not attend. Authorities insist the country's constitution allows Chavez to take the oath of office at a later time.
But the opposition has cried foul, calling for a medical board to review the absent leader's health -- a demand rejected by the Supreme Court, which said the delayed swearing-in was constitutional.
In Cuba on Saturday, President Raul Castro voiced his support for the Venezuelan leadership, his government's closest and most critical economic and political ally.
Castro comments came during a meeting with Venezuelan Vice President Nicolas Maduro, who arrived in the Cuban capital late Friday to check on his boss.
Raul Castro "expressed his confidence in the ability of the Venezuelan people and their institutions to address and overcome any challenge," a government statement said.
"Raul and Maduro shared their mutual satisfaction with the emotional demonstration of support for Venezuela and President Chavez on January 10 in Caracas," it added in reference to a mass rally on the Venezuelan capital.
At a Mass for Chavez in Havana late Saturday, priest Yosvany Carvajal asked God to bless him, stay at his side and ensure a swift recovery. Worshipers included Venezuelan Ambassador Edgardo Ramirez and Alex Castro, son and personal photographer of retired revolutionary icon Fidel Castro.
Two Chavez allies, Argentine President Cristina Kirchner and Peruvian President Ollanta Humala, also arrived in Havana Friday.
"We all hope for a quick recovery," Humala said.
Kirchner refused to comment on Chavez's health when asked by reporters Saturday, saying it should be left to his family. She did, however, thank Castro, 86, for hosting a luncheon for her in his home the previous day.
Like Chavez, Castro has been sidelined by health problems and rarely appears in public since stepping aside as president of the communist country in 2006.
Throughout his illness, first detected in June 2011, Chavez -- in power for 14 years -- has refused to relinquish the powers of the presidency, even when leaving for Cuba for his latest surgery.
The Venezuelan constitution says new elections must be held within 30 days if the president-elect or president dies or is permanently incapacitated, either before he takes office or in the first four years of his six-year term.