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The meeting, widely interpreted as an attempt to reset relations and rebuild trust, follows an extended period of diplomatic estrangement between the two neighboring nuclear powers.
"The common interests of China and India far outweigh their differences ... Of course Xi and Modi will also address each other's concerns, but they are not likely to indulge in strategic distrust and geopolitical competition," the opinion piece said.
On Friday afternoon, Modi and Xi had a one-on-one meeting before touring the Hubei Provincial Museum in Wuhan, home to some of China's oldest cultural relics.
Other pictures showed Xi accompanying Modi throughout the exhibition as the Indian leader played musical instruments and viewed the displays.
Busy schedule planned for summit
Joined by China's foreign affairs heavyweights Yang Jiechi and State Councilor Wang Yi, Modi and Xi began a second round of talks at the East Lake guesthouse later in the evening.
According to a schedule released by the Indian Foreign Ministry, Xi and Modi have a total of six engagements planned over the two-day period.
On Saturday, they are expected to hold a second one-on-one meeting at a state guesthouse on the banks of the East Lake, followed by a boat ride.
Modi said on his official Twitter account, ahead of his departure, the meeting would provide the two leaders with an opportunity to exchange views on a range of issues of "bilateral and global importance."
"We will also review the developments in India-China relations from a strategic and long-term perspective," added Modi.
But an Indian opposition leader sent a cheeky warning to Modi after the Indian Prime Minister had touched down in China, reminding him to mention India's "crucial issues" to Xi, including the border dispute at Doklam and China's large-scale economic investment in Pakistan.
According to Indian media reports, a joint statement will not be issued following the visit.
Closer trade ties
Unlike a more traditional state visit, the casual setting appears to have been arranged in a bid to avoid potentially complex policy negotiations.
Writing in the Hindustan Times on the eve of the summit, Chinese Ambassador to India, Luo Zhaohui, described the two countries as being at a "critical stage of economic development and modernization," pointing out that economic and trade cooperation between the two nations has surged in recent years.
China is India's largest trading partner with a total of $84 billion in bilateral trade last year. But the economic relationship is dwarfed by the US-China trade volume, which stood almost $600 billion.
Referencing the rising threat of US protectionism, Luo stressed the importance of maintaining free and open cross-border trade. "With the current backlash against globalization, a heart-to-heart dialogue between the two leaders will promote free trade," read the op-ed.
Whether Modi and Xi can work to develop closer trade ties, will depend to some extent on their ability to overcome more lasting, politically sensitive issues.
Doklam standoff
Tensions between India and China rapidly escalated in July over a thin strip of land bordering both countries, as well as the kingdom of Bhutan, in the Himalayas.
Bhutan accused the Chinese government of violating its treaty obligations by building a road inside Bhutan's territory. Beijing denied the accusation, saying the area -- known as Doklam -- was Chinese territory.
India and Bhutan have historically strong relations and the situation quickly grew more serious, as both countries increased their military presence on the border.
The Doklam standoff was the latest in a long-running series of territorial flare-ups between the two superpower neighbors.
In 1962, China and India engaged in a bloody border war, and skirmishes have continued to break out sporadically in the decades since.