Modi conveyed India's desire to maintain peace at the border, while the two neighbours work at attempting to finding a solution to their border dispute.
At the meeting in Brazil, which was to have lasted about 40 minutes but stretched to 80, the Chinese President invited PM Modi to Beijing for a summit of Asia and Pacific (APEC) leaders in November.
Modi posted a picture of the meeting and tweeted, "Had a very fruitful meeting with Chinese President Mr. Xi Jinping. We discussed a wide range of issues."
During his campaign for the general elections this year, Modi had taken a strident position on incursions by the Chinese army into Indian territory and had warned China against its "expansionist designs”.
But in the Brazilian town of Fortaleza, ahead of the sixth BRICS summit, Modi engaged diplomatic levers to convey his message. This is the new PM's first foreign visit with multilateral engagements. BRICS or Brazil, Russia, India, China, South Africa is a group of emerging economies.
Over the last five decades, New Delhi has accused China of occupying 38,000 sq km of Indian territory, while Beijing lays claim to 90,000 sq km of land in Arunachal Pradesh. Last year, tension escalated when India alleged that Chinese troops had crossed over into the Ladakh region.
Prime Minister Modi emphasized on boosting economics and better relations between the two countries will remain his top priority.
The Chinese president accolades the meeting by observing that when China and India meet, the world watches.
PM Modi has invited Xi to India and the Chinese President has accepted the invitation. India will also get back on Mr Xi's invitation for the APEC summit after checking the PM's engagements then.
