The two leaders engaged in what was described as "good discussions and good meeting".
The meeting, first between the two leaders, was scheduled for 40 minutes but went on for 80 minutes as it was a free-wheeling discussion without any constraints.
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"Had a very fruitful meeting with Chinese President Mr Xi Jinping. We discussed a wide range of issues," Modi said on micro-blogging website Twitter after the meeting with Xi.
A statement issued by the Prime Minister's Office said, "Both sides emphasised on the need to find a solution to the boundary question. The Prime Minister stressed the importance of strengthening mutual trust and confidence, and maintaining peace and tranquility on the border.