The Union Minister of Women and Child Development had said in a letter to Jayalalithaa that she would be happy to do anything "to make this time less onerous."
In her reply to Gandhi, Jayalalithaa said the letter "touched me deeply."
"I was especially moved by the fact that, despite your busy schedule as Union Minister, Ministry of Women and Child Development, you found the time to think of me and send your heartwarming missive."
The 66 year-old former Chief Minister also thanked Tamil icon Rajnikanth for his "kind and gracious sentiments."
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"I pray that the Almighty may bless you with long life, good health, prosperity and success in all your activities. Please convey my best wishes to all the members of your family," Jayalalithaa told Rajnikanth.
On Sunday, the AIADMK had released the letters by Gandhi and Rajnikanth to Jayalalithaa. The Union Minister while expressing her support and sympathy with the party supremo had said that she would be happy to do anything "to make this time less onerous."
Rajnikanth, also a resident of Poes Garden, had said he was "glad" to see the former Chief Minister back in her residence.
Jayalalithaa had stepped out of a Bangalore Jail on Saturday after the Supreme Court granted her bail in the Rs 66.65 crore disproportionate assets case.