The two leaders, who arrived almost at the same time in this seaside city of Brazil last evening to attend the BRICS Summit, engaged shortly thereafter for what was described as "good discussions and good meeting".
The meeting - first between the two leaders - was scheduled for 40 minutes but it went on for 80 minutes as it was freewheeling discussion without any constraints.
"Had a very fruitful meeting with Chinese President Mr. Xi Jinping. We discussed a wide range of issues," Modi tweeted after the meeting with Xi, also the General Secretary of the ruling Communist Party of China.
Prime Minister Modi told Xi that "if India and China could amicably resolve the Boundary Question, it would set an example for the entire world, on peaceful conflict resolution," the statement added.
The two sides have held 17 rounds of the Special Representative talks aimed at resolving the boundary issue.
India asserts that the border dispute covered nearly 4,057-km long Line of Actual Control, while China claims that it confined to about 2,000 km to the area of Arunachal Pradesh, which it refers as Southern Tibet.
During the meeting, Modi also suggested the addition of one more route for the Kailash-Mansarovar Yatra in Tibet, keeping in view the terrain difficulties.
President Xi "accepted this as a suggestion for consideration," the statement said.
The Yatra involves trekking at high altitudes of up to 19,500 feet under arduous conditions.
APEC includes Canada, Mexico, Russia and the United States and accounts for about 40% of the world's population, 55% of global gross domestic product and 44% of world trade.
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