Kovind, who was accompanied by his wife and daughter, was received at the temple gate by the priest and other officials with the traditional "Poorna Kumbha Mariyathai" (temple honours).
"It has been a pleasure to visit this historic and holy temple which signifies that good always prevails over evil...the visit has filled me with immense peace and happiness.... My appreciation to all those who work tirelessly to maintain the splendour of this temple," Kovind wrote in the visitors' book at the temple.
Later, he visited the memorial of former president A P J Abdul Kalam at Pei Karumbu and paid homage to the latter.
In the visitors' book there, Kovind wrote, "It is a personal privilege and honour to be able to offer prayers and pay homage to my predecessor -- a great scientist and son of the soil -- at the National Memorial."
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He also described the memorial, built by the Defence Research and Development Organisation (DRDO), as a "major architectural and engineering marvel" and said it was a befitting tribute to Kalam.
During his visit, he also enquired about an autorickshaw driver, Shanmugham, who had taken him on a guided tour of the island town years ago, when Kovind was a Rajya Sabha MP.
A three-tier security cover was in place in view of the president's visit, the police said.
Kovind's itinerary also includes appointments in Chennai.
Earlier, the president arrived by a special flight at Madurai, from where he went to a nearby "Mandapam" by helicopter.