A man walks by a painting on a wall of Venezuelan President Hugo Chavez in Caracas on January 9.

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Adan Chavez says his brother, President Hugo Chavez, is making strides in his recovery

Chavez, 58, is undergoing cancer treatment in Cuba and battling complications

He has not been seen in public since doctors operated on him a month ago

Argentina's president visits Cuba in a show of solidarity with Chavez

Venezuelan President Hugo Chavez is not in a coma and is continuing to make strides in his recovery, his brother said.

Chavez’s brother, Adan Chavez, who is governor of Chavez’s home state of Barinas, recently returned from Cuba, where the president is undergoing cancer treatment.

Chavez, 58, has not made a public appearance since doctors operated on him a month ago. The long absence is not typical of the loquacious leader, who missed his own inauguration this week.

“The head of state continues to assimilate treatment well and, each day, advances in his recovery,” said Adan Chavez, according to a statement posted Saturday by his office.

He characterized as “totally false” rumors that Chavez is in a coma and that his family was discussing the possibility of taking him off life support.

Last week, a government spokesman said Chavez was battling a severe lung infection that has caused respiratory failure.

“We are sure that with the support of God, science and the people, our president will emerge from this new battle,” the brother said.

His comments came as Argentinian President Cristina Fernandez de Kirchner, an ally of Chavez, visited Cuba in a show of solidarity, and just days after Chavez’s health problems prevented him from being in Caracas for his inauguration ceremony.

Throngs of supporters swore an oath of loyalty in his absence Thursday.

Vice President Nicolas Maduro called on the masses gathered to take an oath of “absolute loyalty to the leadership of Comandante Hugo Chavez.”

The crowd repeated his words, holding thousands of tiny copies of the constitution up in the air.

Opposition politicians have argued that delaying Chavez’s swearing-in without designating a temporary replacement leaves no legitimate leader in charge of Venezuela.

Chavez allies, including a majority of lawmakers in the country’s congress, have said he should remain in power while taking the time he needs to recuperate.

Venezuela’s Supreme Court backed the government’s position, ruling that Chavez began a new term on Thursday and can be sworn in later before the court.

Before he left for Cuba for surgery, Chavez said he wanted Maduro to assume the presidency if he becomes incapacitated and called on voters to support him at the polls.

CNN’s Dana Ford and Catherine E. Shoichet contributed to this report.