After around an hour-long talks at the Fisherman's Cove resort, the two leaders took a stroll along the beach and were seen engaged in discussion. Earlier, Modi and Xi came together to the venue in a golf cart.
Sources said the talks between the two leaders went off well. The tete-e-tete was followed by delegation level discussions.
Xi arrived here in this bustling port city on Friday amid strain in bilateral ties between the two countries after India withdrew Jammu and Kashmir’s special status and bifurcated the state into two Union Territories.
On Friday, Modi and Xi held a two-and-a-half-hour “open and cordial" one-on-one discussion over dinner, vowing to jointly combat terrorism and radicalisation, and expand bilateral trade and investment..
The meeting at the magnificent Shore temple complex under a sea-facing colourful tent went beyond the scheduled time as both leader touched upon a range of issues over sumptuous local delicacies.
"This was quality time that the two leaders spent together one-on-one," Foreign Secretary Vijay Gokhale had said after the meeting, adding vowed to work together so that radicalisation and terrorism do not affect the multi-cultural, multi-ethnic and multi-religious societies of the two nations.
He said the two leaders also deliberated on trade and economic issues with a focus on identifying new areas for investment and enhancing trade volume and value of two-way trade.
The issue of trade deficit and trade imbalance was also discussed, the foreign secretary said.
Earlier on Friday afternoon, Modi, dressed in a Tamil attire of Veshti (Dhoti), white shirt and an ‘angavastram’, took Xi for a guided tour of the famous world heritage sites of Arjuna’s Penance, Krishna's Butterball, the Pancha Ratha and Shore temple in this ancient temple town, kicking off the second informal summit between the two leaders.
“The free flowing nature of the informal summit at the UNESCO world heritage site will continue and deepen contacts at the highest level and guide the future trajectory of India-China relationship," MEA Spokesperson Raveesh Kumar said.
Meanwhile, India has announced a five-year tourist e-visa with multiple entry facility for Chinese travellers, coinciding with President Xi's visit.
"It is anticipated that this unilateral liberalisation of e-TV for Chinese nationals will further enhance people-to-people exchanges between the two countries and encourage more Chinese tourists to choose India as a destination for tourism purposes," the Indian embassy in Beijing said in a press release.
China's state run Xinhua news agency reported that Xi and Modi agreed to promote exchanges and mutual learning among civilizations to achieve joint development and prosperity during their meeting on Friday.
Noting that China-India cultural and people-to-people exchanges bear great potential, the Chinese president urged both countries to take the 70th anniversary of their diplomatic relations next year as an opportunity to conduct broader and deeper cultural and people-to-people exchanges.
The two leaders held an extensive talk on dialogue and mutual learning among civilizations, the Xinhua reported. As he toured the monuments at Mamallapuram with Modi, Xi said Tamil Nadu, a maritime transit hub for cargoes in the ancient Silk Road, has a long history of exchanges with China and close connections with China on maritime trade since ancient times.
Both as ancient civilizations with several thousand years of history, China and India have carried on their exchanges and mutual learning till this day, Xinhua quoted Xi as saying. The two countries' ancestors have overcome various obstacles to carry out extensive exchanges and promote the development of literature, art, philosophy and religion, which have greatly benefited both sides, Xi said. He also called on the two countries to jointly advocate and push forward dialogue and exchanges among different civilizations, so as to inject more lasting driving force into the development of bilateral ties and continue to produce new glory for Asian civilizations, the Xinhua said.
Modi told Xi that the Group of Monuments at Mamallapuram is an outstanding example of India's cultural heritage and architecture, and witnessed India and China's civilization exchanges and historical connections for more than a dozen centuries.
After their development for several thousand years, India and China have both become important emerging economies, Modi said, stressing that enhancing exchanges and cooperation bears great significance to the two countries and will promote global progress and prosperity. The wisdom from the two countries' ancient and profound civilizations can provide inspiration for solving various challenges facing the world today, Xinhua quoted him as saying.
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.
The two leaders agreed that China and India should respect and learn from each other so as to jointly achieve common development and prosperity, as well as the great rejuvenation of the two civilizations, it said. The two leaders held their first informal summit in the central Chinese city of Wuhan in April last year.
Xi’s visit to India came two days after he held talks with Pakistan Prime Minister Imran Khan in Bejing.
After the talks, a joint statement said China is paying “close attention" to the situation in Kashmir and that the issue should be properly and peacefully resolved based on the UN Charter. The comments evoked sharp reaction from New Delhi.
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.
Sources said the two leaders are expected to issue some directions at the end of the summit on Saturday as they did after the first edition of new format of engagement in Chinese city of Wuhan last year.
“Both sides know that a lot is riding on the relationship and this is reflected in the summit being held on schedule despite speculations of its postponement in recent weeks," said a senior official on condition of anonymity.
This story has been published from a wire agency feed without modifications to the text. Only the headline has been changed.