One of Venezuelan President Hugo Chavez's daughters took to social media to demand a halt to "lies" about her father's health after rumors circulated the cancer-embattled leader had died.

"Respect for the family and especially fully respect for my people. Enough of the lies! We are next to papa. LIVING, struggling and recovering his health. WITH GOD," Maria Gabriela Chavez wrote in a Twitter message Friday.

Maria, the second of Chavez's four children, is with the Venezuelan leader in Havana as he recovers from cancer surgery.

Rumors have proliferated online about Chavez's supposed death ever since the 58-year-old president underwent his fourth surgery earlier this month to fight an unspecified cancer.

Vice President Nicolas Maduro, Chavez's handpicked successor, on Friday said that the president was making steady progress.

The latest official health report out Thursday said the respiratory infection that Chavez developed following surgery has been contained and his condition was improving.

Chavez underwent cancer surgery on December 11, scarcely a day-and-a-half after revealing to his stunned countrymen that his cancer had returned and just two months after his triumphant re-election to a six-year term.

The fiery populist leader, who was first diagnosed with the disease in June 2011, had assured Venezuelans that he was cancer-free after three surgeries and debilitating rounds of chemo and radiation therapy.

Significant aspects of Chavez's condition -- including the type, location and severity of his cancer -- have been kept secret, fueling rumors and uncertainty about Venezuela's future.

[Image via Agence France-Presse]