Mr Kovind had separate meetings with Mr Palaniswami and Mr Panneerselvam in which leaders of the two factions of the ruling AIADMK, including School Education Minister KA Sengottaiyan (AIADMK-Amma) and senior AIADMK-Puratchi Thalaivi Amma leader E Madhusudanan participated.
Followers of party Deputy General Secretary TTV Dinakaran were also there.
Both Mr Palaniswami and Mr Panneerselvam in their respective speeches recalled the good ties and friendship between Prime Minister Narendra Modi and late Chief Minister Jayalalithaa.
Praising Mr Kovind, the chief minister said he overcame socio-economic barriers and made his way up through hard work, honesty and dedication.
Mr Panneerselvam said, "Though his victory is assured, we express our appreciation for his (Kovind's) political decency in visiting us to seek our support."
Recalling the friendship between PM Modi and Jayalalithaa, he said his party's support to Kovind was its reflection.
The former chief minister hailed Mr Kovind for his administrative abilities and said if Amma were alive, she would have supported Kovind's candidature.
Mr Kovind thanked the leaders for their support to his candidature.
Earlier in the day, Mr Kovind met Puducherry legislators and the lone Lok Sabha member from the Union Territory.
Puducherry-based All India NR Congress chief N Rangasamy and his party legislators met Kovind at a hotel.
Puducherry's lone Lok Sabha MP R Radhakrishnan, who belongs to the main opposition party in the Assembly (AINRC), was also present there, according to Tamil Nadu BJP.
Also, BJP's lone legislator from Kerala and veteran party leader O Rajagopal took part in the meeting to drum up support for Mr Kovind.