President Xi also called for putting India-China relations on the "right track", according to the official Xinhua news agency.
China is prepared to work with India to seek guidance from the five principles of the Panchsheel Agreement, Xi assured PM Modi as they held their first substantive bilateral meeting after the Doklam standoff, which had put ties between the two countries under strain.
The prime minister, accompanied by senior officials including National Security Advisor Ajit Doval and Foreign Secretary S Jaishankar, met the Chinese leader just before his travel to Myanmar from this port city.
During their meeting, Modi congratulated Xi on a "very successful" BRICS Summit, China's state-run Xinhua news agency reported.
Narendra Modi (@narendramodi) September 5, 2017
The various deliberations during the BRICS Summit were extremely productive. Looking forward to building on these in the times to come.— Narendra Modi (@narendramodi) September 5, 2017
I thank the Chinese government & people for their warm hospitality during the BRICS Summit. Leaving for Myanmar for a bilateral visit.— Narendra Modi (@narendramodi) September 5, 2017
The meeting comes amid diplomatic efforts by the two sides to overcome the bitterness caused by the 73-day face-off between their troops in the Doklam area of the Sikkim sector.
The Chinese and the Indian troops were engaged in a standoff since June 16 after the Indian side stopped the construction of a road by the Chinese Army.
On August 28, India's External Affairs Ministry announced that New Delhi and Beijing have decided on "expeditious disengagement" of their border troops in the disputed Dokalam area.
Indian officials had earlier indicated that the two leaders were expected to discuss ways to create confidence building measures. The sense is that both countries want to "move on" after the standoff.
Earlier, Modi also held a bilateral meeting with Egyptian President Abdel Fattah el-Sisi.