The leaders also pledged to strengthen trade and diplomatic ties during the 80-minute meeting in Fortaleza, their first since nationalist hardliner Modi won landslide elections in May.
"Both sides emphasised on the need to find a solution to the Boundary Question," the Indian government said in a statement in New Delhi.
"The Prime Minister stressed the importance of strengthening mutual trust and confidence, and maintaining peace and tranquility on the border."
Modi said in a tweet he had "a very fruitful meeting" with Xi and they had discussed a wide range of issues.
Had a very fruitful meeting with Chinese President Mr. Xi Jinping. We discussed a wide range of issues pic.twitter.com/dL6n0p17TO
— Narendra Modi (@narendramodi) July 15, 2014
Ties between the nuclear-armed giants have long been soured by border disputes and competition for influence in their neighbourhood.
Soon after coming to power, Modi invited Xi to visit India later this year, while China's foreign minister has travelled to Delhi for talks with the prime minister.
Leaders of the BRICS group of emerging powers are to meet Tuesday in Fortaleza to launch a new development bank and a reserve fund seen as counterweights to Western-led financial institutions.
During the bilateral talks, Modi accepted Xi's invitation to visit Beijing later this year, Indian foreign ministry spokesperson Syed Akbaruddin said.
Xi also invited Modi to attend the Asia Pacific Economic Cooperation forum in Beijing in November, although India is not a member, Akbaruddin told reporters in Fortaleza, in a briefing shown on Indian TV.
Modi stressed the need to address a trade imbalance between the two countries, which is heavily skewed in China's favour.
Modi, whose new government has pledged to boost road, rail and port projects, called for enhanced Chinese investment in Indian infrastructure, the Delhi statement said.
Xi agreed the need for balanced trade and said "enhanced services exports from India to China could be one way to address the issue".
China is India's biggest trading partner.
But relations are still dogged by mutual suspicion - a legacy of a brief but bloody war in 1962 over the Indian state of Arunachal Pradesh in the eastern Himalayas that China claims as its own.
COMMENTS (9)
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@Bewildered: Because trade with Pakistan is too insignificant.
@Bewildered: China never says that resolve the core issues or else no buiness. Both India and China despite major issues of Aksai Chin and Arunachal Pradesh are involved in doing billions of dollars of business. Both nations understand the need of moving forward setting aside the differences and try to resolve the issues. If both nations get stuck like Pakistan that says either resolve kashmir issue or no business... then perhaps India-china would be the same as India-Pakistan today. And the solution to kashmir issue will come only after realizing that Kashmir is India's "Atoot Ang".
@Bewildered: Pakistan exports to India were about 513 million USD and imports were 1.8 billion USD. So the ratio is 30:70, and decreasing. Apart from this there is a trade of about 4 billion USD between the two countries through Dubai.
http://tribune.com.pk/story/548768/trade-between-india-and-pakistan-surges-21-to-2-4-billion/
@Bewildered:
Ah Genius, then why are you wasting time in talks, go ahead solve it, India has claim on Aksai Chin, India did not control Aksai Chin, China has claim on AP aka South Tibet (and rightly so) China did not control AP.
Pakistan calls for a UN mandated Solution of Kashmir dispute according to wishes of People of Jammu & Kashmir, which India accepted but never implement it.
What Pakistan has to loose with all this in Aksai Chin & South Tibet (AP)?
regards,
@Bewildered: Geez. You really are bewildered,
"Indian Prime Minister Narendra Modi and Chinese President Xi Jinping agreed on the need to resolve a decades-old border dispute during talks before the BRICS summit in Brazil"
With China, India talks about resolving disputes, but with Pakistan maintaining status-quo. What a hypocrite country. Let's see if India retracts her claim on Aksichen and other disputed territories, or China vacates the territories claimed by India.
"Modi stressed the need to address a trade imbalance between the two countries, which is heavily skewed in China’s favour."
India never talks of TRADE IMBALANCE with Pakistan which is heavily tilted in favor of India (90% vs. 10%), but funnily demands even more access from Pakistan as if the balance is other way round. Obviously Indians never care about principles and ethics. It is the duty Pakistani government to take care of Pakistan's national interests, and demand for trade balance as the Indians do.
Deeper than Indian/Atlantic Ocean and sweeter than Sugarcane.