"Amma (Jayalalithaa) is well. God has given her good health and we are very happy," AIADMK spokesperson CR Saraswathy told reporters.
Meanwhile, Vijay said Jayalalithaa was "recovering fast" and would resume work soon.
"I have specially brought holy water of lake Manasarovar of Mount Kailash for the Chief Minister. Amma is recovering very fast. Very soon (she will be) out of hospital and start working," he said.
Vijay said that the "prayers of millions of people are working and she will be very well."
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Later, the hospital had said she was being treated for infection with respiratory support, among others.
Specialists from All India Institute of Medical Sciences, New Delhi, and from London, among others, have treated her during the period.
On the condition in which Jayalalithaa was admitted to
the hospital, it said that at around 10 PM on September 22, 2016, Apollo Hospitals received a call from the residence of the then chief minister.
When the ambulance reached there, they found her breathless with low oxygen saturation, resulting in drowsiness.
There were pre-existing co-morbidities like diabetes, hypertension, asthmatic bronchitis and hypothyroidism, but clearly the "treatment report of Apollo Hospital, as well as that of AIIMS do not mention any evidence of trauma or any other event as alleged by certain political leaders," he said.