The Chief Minister “is interacting (with people) and progressing gradually”, said a medical bulletin, the first issued after a 11-day gap.
AIADMK leaders including C. Ponnaian have told the media that Jayalalithaa was talking to people and had even sat up.
He said the AIADMK chief would be home in a few days.
The hospital said the Chief Minister continued to be under treatment and observation.
A team of experts of the critical care group, cardiologists, respiratory physicians, consultants of the infectious diseases department, endocrinologist and dialectologist of the hospital were treating her, the bulletin said.
Jayalalithaa was admitted to the hospital a month ago with fever.