"The current structure of global governance looks like a pyramid," he told the gathering in New Delhi in Saturday.
"At its top are concentrated power and decision-making. And at the bottom are those countries that are affected by these decisions, but cannot shape them," he said.
The plenary session brought together, in the main hall of the Bharat Mandapam convention center, Chinese President Xi Jinping, Russian President Vladimir Putin and Iranian President Masoud Pezeshkian, among other heads of state of the bloc.
Modi stated that the roadmap must be articulated around three axes - representation, responsiveness, and rule-making - to increase the weight of emerging economies in international institutions.
"The reform of the United Nations Security Council can no longer be postponed," stressed the Indian leader, who called for linking negotiations on its reform to defined deadlines and concrete results.
Modi also demanded that the voting power, leadership positions, and priorities of international financial institutions better reflect the current weight of the economies driving global growth.
India, which holds the rotating presidency of the bloc this year, advocated for BRICS to translate its internal consensus into concrete global outcomes and for the Global South to move beyond merely accepting norms to also participating in their formulation.
"The Global South is at the forefront of global crises today, but at the back of decision-making," Modi said, before calling for the existing "pyramid of privilege" to convert into a "platform for partnership."
The prime minister also stressed that the BRICS were "not against anyone" and must move forward by incorporating everyone, a formulation with which New Delhi seeks to present the bloc as a platform for reforming the international system and not as an alliance of confrontation.
In his address to the summit, President Xi called on the BRICS bloc to be a peacemaker in the Middle East conflict.
China will work with other BRICS members in that role, as the war "does not serve the common interests of the international community", state-run CCTV quoted Xi as saying.
The BRICS group includes Brazil, Russia, India, China and South Africa, Egypt, Ethiopia, Indonesia, Iran and the United Arab Emirates.
It was set up in 2009 to challenge a world order dominated by the United States and its Western allies. Together, its members account for more than 40 per cent of the world's population and almost a quarter of the global economy.
The Chinese leader called the bloc a "leading group" in the Global South and a model of self-reliance among emerging and developing countries that should promote innovation-driven development.
He said China would assume the BRICS chairmanship next year, and host the 19th summit.
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