In a statement issued here, the hospital said:
"The Honourable Chief Minister is responding well to the treatment and continues to get better. As part of ongoing recuperation, the Honourable Chief Minister has been advised few more days of rest."
The hospital said Jayalalithaa, who was admitted on Thursday after suffering from fever and dehydration, is under observation.
According to Apollo Hospitals, Jayalalithaa will be discharged from the hospital in a few days and would resume normal official duties soon.
Dismissing as "baseless" rumours in the social media that Jayalalithaa has been taken abroad for treatment, the hospital said: "There is no question of taking the Honourable Chief Minister abroad for treatment, as there is no necessity at all for this."
According to the statement, necessary medications are being administered and necessary tests and investigations are being done to prevent recurrence of fever.
Jayalalithaa is on normal diet and she has no fever, the statement added.