The Prime Minister first launched the National Handloom Day celebrations at the University of Madras here and then drove straight to the Chief Minister's residence where she warmly welcomed him at the doorstep.
Sources said the AIADMK leader had invited the Prime Minister for lunch, which he accepted.
During the discussions, she is understood to have taken up issues concerning Tamil Nadu including inter-state river disputes with Karnataka and Kerala and presented a memorandum.
AIADMK has 37 members in the Lok Sabha and 11 in the Upper House.
Earlier in day, Jayalalithaa had welcomed Modi at the airport.
During his address at the function where Jayalalithaa was not present, the Prime Minister thanked "Dr Jayalalithaa", the state government and the people of Tamil Nadu for successfully organising the event.