The two leaders sat on the lawn at the temple and exchanged views on development and cooperation.
In his delegation level talks with Xi at a luxury resort overlooking the Bay of Bengal in Kovalam on the second and final day of the informal summit, Modi noted that India and China were global economic powers during most of the last 2000 years and were returning to stage gradually.
Foreign ministry spokesman Raveesh Kumar called it "a highly productive day".
Xi and Modi visited three iconic monuments - Arjuna's Penance, Pancha Rathas and the Shore Temple - at Mamallapuram, a tourist town famous for its stone carvings 60 kilometers south of Chennai.
Friday's talks between Modi and Xi were aimed at building on the relationship reset that began in Wuhan in April previous year. No agreements are expected, giving the leaders the time they need to discuss all the matters that they want to.More news: MSNBC news reporter interrupted by her child while presenting live on air
In their first informal meeting a year ago, the two leaders reached the consensus that the differences between the two countries should not be allowed to turn into disputes. The two leaders had a 70-minute conversation at Chennai's Mamallapuram this morning but their overall one-on-one discussions over the last two days have exceeded five hours.
Officials on both sides said the focus of the Modi-Xi summit has been to move forward and chart a new pathway of development notwithstanding sharp differences between the two countries over several contentious issues.
"The Wuhan spirit had given a new momentum and trust to our ties".
Ties were ruffled when India revoked the special status of the Himalayan territory of Kashmir in August, angering both Pakistan, which claims the region, and its all-weather ally China.
Modi and Xi are meeting in the southern town of Mamallapuram, home to centuries old wind-swept temple monuments but also popular with tourists for surfing in its flawless waves.More news: Trump authorizes administration to slap 'significant' sanctions on Turkey
When Mr Xi said he supports Pakistan's "legitimate rights", India's foreign ministry thundered it was "not for other countries to comment on the internal affairs of India".
But since Wuhan other irritants have emerged, including a reported "scuffle" in Ladakh last month and Indian military activities in the northern Indian state of Arunachal Pradesh, part of which Beijing claims.
Xi recalled his successful meeting with Modi in Wuhan a year ago, which brought China-India relations into a new stage, and said that he is delighted to come to Tamil Nadu in southern India to further learn about the country.
In 2017, Delhi and Beijing faced off for two months on the Doklam plateau - claimed by China and Bhutan - when Chinese troops started building a road and India sent its forces to halt them. Earlier, Modi and Xi came together to the venue in a golf cart. In contrast, Xi is in India for less than 24 hours.More news: Renault removes Thierry Bolloré as CEO
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