0843 GMT January 25, 2020
Xi and Modi strolled along a pristine Bay of Bengal beach and held one-on-one talks from chairs overlooking the ocean before their delegations sat down to official negotiations at the historic resort town of Mahabalipuram, south of Chennai, AFP reported.
The two leaders met for the second time in 18 months in a bid to ease tensions over border disputes, the troubled Kashmir region and China's domination of trade between their huge economies.
They reaffirmed a pledge made at the last summit in Wuhan, China, that "both sides will prudently manage their differences and not allow differences on any issue to become disputes," said an Indian government statement.
Modi said the Wuhan summit had given "increased stability and fresh momentum to our relationship".
"Our Chennai vision today has launched a new era of cooperation between our two countries," he added.
Xi said in his opening remarks to the summit delegations that he and Modi held "candid discussions as friends."
The buildup to the summit has been dominated by India's move in August to end the autonomous status of the Jammu and Kashmir state.
Changes ordered by the New Delhi government will see Kashmir's Ladakh region – part of which is claimed by Beijing – turned into a separate Indian administrative territory.
India has moved closer to the United States and its allies in seeking a counter-weight to China's growing military shadow in the Asia-Pacific region.
It has been infuriated by China's backing for Pakistan, which controls a large chunk of Muslim-majority Kashmir.
The Himalayan region has been a long-standing source of conflict between India and Pakistan. China's proposal for major infrastructure building in Pakistan-occupied Kashmir as part of its Belt and Road Program has faced strong Indian opposition.
China is in turn sensitive to India letting the Tibetan spiritual leader the Dalai Lama keep his base in northern India.
But most of the disagreements were pushed to one side so they did not become a summit dispute.
Kashmir was not raised in the two days of talks, Indian Foreign Secretary Vijay Gokhale said.
They did however agree to step up their efforts so "that the international community strengthens the framework against training, financing and supporting terrorist groups throughout the world," said the Indian statement.
Modern rivalry between the world's two most populous countries dates back decades.
They went to war in 1962 over disputed Himalayan territory and other border standoffs remain. In 2017, the Indian and Chinese armies faced each other down for more than two months on a high altitude border plateau claimed by China and India's tiny Himalayan ally Bhutan.