The two leaders held their first meeting on Friday, where Modi's attire stole much of the show, donning a traditional outfit known as a "veshti".
Prime Minister Modi presented a specially woven shawl to President Xi Jinping, depicting the portrait of the visitor.
The second informal India-China Summit will end with a lunch on Saturday afternoon and both the sides will be issuing separate statements. "This will benefit the people of our nations and the world", he said.
Meanwhile, to deepen bilateral relations, both Modi and Xi have decided that the 70th anniversary of the establishment of India-China relations in 2020 will be utilised to deepen exchanges at all levels including legislatures, political parties, cultural and youth organisations and militaries. Wuhan spirit has given our ties a new momentum and trust.
Xi said in his opening remarks to the summit delegations that he and Modi held "candid discussions as friends".
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"There was a good conversation on trade, an issue of concern; President Xi said China is ready to take honest action in this regard and discuss in a concrete way how to reduce the deficit", he said. Earlier, Modi and Xi came together to the venue in a golf cart.
Modi released a short video on Twitter showing him walking barefoot in the sand, collecting the trash in a bag on Saturday morning in Mamallapuram in Tamil Nadu state.
"Both leaders agreed that it was important to deal with the challenges of terrorism and radicalisation in an increasingly complex world". Both Xi and Modi said the two countries need to look to the future.
"One of the important understanding which was reached between the two leaders was that a new mechanism will be established to discuss trade, investment and services, at an elevated level".
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The programme showcased the Indian classical dance forms of Kathakali and Bharatnatyam to fast-paced Carnatic music, highlighting the region's magnificent roots.Xi will head to Nepal from Chennai.
India and China have been at odds over the disputed Ladakh region in Kashmir, which sits on the Indo-Chinese border and has been the setting for conflict between the two countries for decades. "Radicalisation is a major concern for both, and both would work together to see that radicalisation and terrorism did not affect the fabric of our multicultural, multi-ethnic societies". The bilateral trade between India and China is about $87 billion.
The high-level panel will have Finance Minister Nirmala Sitharaman will be part of it alongside Vice Premier of China. "Today, our Chennai vision will begin a new age in relations between our two countries".
In the Shore Temple on the coast of the Indian Ocean, Xi and Modi talked about the domestic development of China and India and exchanged experience in state governance, it said.
Modi launched a "Clean India" campaign after he became prime minister in 2014. Increased Beijing-New Delhi integration could infuriate US President Trump however, as Washington continues to warn its allies to steer clear of Chinese telecommunications company Huawei. Seventy events will be held in the two countries - 35 on each side -to broad base people-to-people contact.
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Chief of Patrol Rodney Harrison said police have received no complaints in recent years about activity at the illegal spot. Four homeless men were beaten to death by another homeless man in the Chinatown section of Lower Manhattan last Saturday.
The two leaders held their first informal summit in the central Chinese city of Wuhan in April a year ago.