Speculation about Mr Chavez's condition has been mounting ever since he underwent an operation on June 10, for what his government has said was a pelvic abscess.
He remained uncharacteristically silent after the operation, even as Venezuela was hit by prison riots that killed at least 25 people and an electricity crisis, before messages began to appear again on his Twitter account on Friday.
A US-intelligence source told the Miami-based newspaper El Nuevo Herald that Mr Chavez "is in critical condition; not on the brink of death, but critical indeed, and complicated."
The newspaper said its sources could not confirm rumours that Mr Chavez may be receiving treatment for prostate cancer in Havana.
