Chavez`s government said he had an operation for a pelvic abscess on June 10 and continues to mend.
"He is recovering," Information Minister Andres Izarra told AFP in the wake of a report by Miami`s El Nuevo Herald citing unnamed US intelligence sources as saying the 56-year-old "is in critical condition -- not on the brink of death, but critical indeed."
The newspaper also said the sources refused to comment on rumors in Venezuela that Chavez could be receiving treatment for prostate cancer.
The Venezuelan government has not addressed details of Chavez`s condition, and angry opposition lawmakers in Caracas say it is unconstitutional for the president to be governing from abroad.
But several top Venezuelan figures have dismissed the reports.
The president of the National Assembly, Fernando Soto Rojas, denied the cancer rumors, saying he was confident Chavez would be back on July 5.
"You`ll see, we`ll have him back here in Venezuela at full strength in just a few days," he said.
Sunday masses were celebrated across the country, along with indigenous rituals that wished the president a good recovery.
"Chavez will be around for a long time," Vice President Elias Jaua told reporters.
The president`s brother, meanwhile, has told Venezuelan state media that Chavez could return to Caracas in about two weeks.
Speaking from Chavez`s home region of Barinas in the west, his mother Elena Frias also said she prayed for a speedy recovery.
"Blessings for my beloved son. May the power of my blessed God heal him and bring him home to me quickly," she said.
And Izarra urged his Twitter followers to not repeat rumors, saying Chavez "is recovering well from his operation."
The Venezuelan president`s enemies "should stop dreaming, and his friends should stop being nervous," senior diplomat Temir Porras tweeted.
Chavez himself fired off a brief Twitter message saying that his daughter and three grandchildren had arrived in Cuba to visit him.
The uncharacteristic silence from someone known for his verbal omnipresence left some foes speculating that Chavez might have had plastic surgery, or might want to drum up sympathy for his illness ahead of a 2012 election in which he will seek a third term.
He had been rushed into emergency surgery during a scheduled visit to Cuba after suffering sharp pain diagnosed as a pelvic abscess that required immediate surgery.
Chavez is Communist Cuba`s main economic and political ally. His cut-rate oil keeps the cash-strapped and isolated Raul Castro regime afloat. (*)
Editor: Kunto Wibisono
Copyright © ANTARA 2011