Xi greeted Modi at a Hubei province museum in the city of Wuhan for what has been billed as an "informal summit" that will continue on Saturday.
While last year's high-altitude standoff in the Himalayas has been resolved, the world's most populous countries have a long history of mistrust.
New Delhi has also raised concerns about Beijing's Belt and Road initiative, a global trade infrastructure programme that includes a major project through Azad Jammu and Kashmir (AJK).
However, the two leaders discussed "strengthening the exchanges and mutual learning between the two civilisations of China and India and promoting the harmonious coexistence and dialogue of different civilisations," the official Xinhua news agency said on its social media account.
Following the museum tour, Modi and Xi were due to hold talks and have dinner together, according to the prime minister's official agenda. On Saturday, they will walk along the East Lake, ride a boat and have lunch together.
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The summit "is New Delhi's well-intentioned attempt to reach out to Beijing to see if the past can be put behind and if the relationship can be reset," Harsh Pant, international relations professor at King's College London, told AFP.
In a statement before leaving India, Modi said he would exchange views with Xi on a range of bilateral and global issues.
"We will discuss our respective visions and priorities for national development, particularly in the context of current and future international situation," Modi said.
Chinese foreign ministry spokesman Lu Kang said Tuesday that the two leaders have "a good working relationship and personal friendship".
They agreed that an informal summit would be conducive to having "full and in-depth exchanges on major issues of common concern in a suitable atmosphere", Lu said.
Both nations say they are committed to solving long-standing border disagreements through dialogue, but progress has been glacial.
India and China went to war in 1962 over Arunachal Pradesh, with Chinese troops temporarily capturing part of the Himalayan territory.
The dispute remains unresolved, with India considering Arunachal Pradesh one of its northeastern states while China stakes claim to about 90,000 square kilometres of the area.
In February Beijing lodged an angry protest with New Delhi over a trip by Modi to the state.
Last year, Indian and Chinese troops faced off on the Doklam plateau, an area high in the Himalayas claimed both by China and by India's ally Bhutan.
The dispute began in June when Chinese troops started building a road on the plateau and India deployed troops to stop the project.
A crisis was averted in August when the two nuclear-armed nations pulled back.
"We have to step out of the shadows of the 1962 war," said Wang Dehua, a South and Central Asia expert at the Shanghai Academy of Social Sciences.
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"The meeting will focus on avoiding the unhappy events we saw in Doklam last year," Wang said.
Chinese defence ministry spokesman Wu Qian said Thursday that the people of both countries share the aspiration of maintaining peace in the border areas.
He said Beijing was willing to enhance mutual trust "despite some difficulties and obstacles in the bilateral military relationship", according to the official Xinhua news agency.
Modi is expected to return to China in June for the summit of the Shanghai Cooperation Organisation, a security bloc led by Beijing and Moscow.
Indian analysts point to a pragmatic reason for Modi to want better relations with China: he faces national elections next year, and he would be better off with stable ties with the world's second-largest economy.
"I don't think he would like to go into an election with the kind of relationship, the low point it had reached over the last year," Pant said.
With China facing a potential tariff war with the United States, Beijing and New Delhi could find common ground on international trade, Pant said.
"It is one of the issues where India and China have worked together on the global stage in the past," he said.
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