Mr Jinping appeared to take a reconciliatory tone when he, without directly referring to the recent Doklam standoff with India, said "peace and development" should be the underpin to resolve issues as the world does not want "conflict and confrontation."
"We the BRICS countries should show our responsibilities to uphold global peace and stability," he said.
PM Modi and Mr Jinping are expected to meet on Tuesday, nearly a week after the two countries ended the 73-day-long Doklam standoff.
After the bilateral with the host, PM Modi will be travelling to Myanmar on a bilateral visit. Chinese and Indian troops had been locked in a standoff in Sikkim sector after Indian troops stopped construction of a road by China's army.
On August 28, the External Affairs Ministry announced that New Delhi and Beijing have decided on "expeditious disengagement" of border troops in Doklam.
Mr Jinping also called on BRICS countries to take a constructive part in the process of resolving geopolitical "hotspot issues". India is also expected to raise its concerns over terrorism at the BRICS Summit, with PM Modi asserting that the group of nations has to make important contributions in upholding peace and security, and address global challenges.
On China's comments that it will not be appropriate to discuss Pakistan's counter-terrorism records at the BRICS Summit, External Affairs Ministry Spokesperson Raveesh Kumar said he cannot pre-empt what PM Modi will say during his interventions at the restricted and plenary sessions of the summit.
Mr Kumar, however, said India's position on terrorism has been very clear and it has been raising the issue at multilateral forums.
Ahead of the summit, Chinese Foreign Ministry spokesperson Hua Chunying had said, "We noticed that India, when it comes to Pakistan's counter-terrorism, has some concerns. I don't think this is an appropriate topic to be discussed at BRICS summit."