In a statement issued in Chennai, the Tamil Nadu government said the Bharatiya Janata Party leader called Jayalalithaa on Sunday afternoon and thanked her for her wishes.
He congratulated Jayalalithaa on her AIADMK's remarkable victory in the general elections. The party won 37 of the 39 Lok Sabha seats in Tamil Nadu.
Modi assured Jayalalithaa that there will be "absolute cooperation between the government of India and the government of Tamil Nadu", the statement said.
On her part, Jayalalithaa wished Modi a successful tenure as the prime minister.