The Brics economies have been hit by falling global demand and lower commodity prices, while some have faced corruption scandals.
Brazil and Russia are both in recession, and Brazil on some counts is suffering its worst downturn since the 1930s.
South Africa narrowly avoided a recession last month, while China is going through its slowest economic growth in 25 years.
Still, Lord Jim O'Neill, the economist who coined the term "Brics", told the BBC he remained confident of the grouping's success.
Ahead of the talks, he said it is "bigger today [than] even in the most optimistic scenario I thought 15 years ago, and it's primarily because of China".
'Asian century'
At the summit, the Brics leaders agreed to set up a new credit rating agency and expand the role of emerging economies, and recognised the threat from terrorism.
In separate agreements, Mr Xi vowed to pursue closer ties with India and Russia as part of a wider Chinese push to foster global trade partnerships.
Indian Prime Minister Narendra Modi said India and China had a responsibility to join hands and turn the 21st Century into an Asian century.
Meanwhile, Mr Modi and Russian President Vladimir Putin signed multi-billion dollar energy and defence pacts on Saturday on the sidelines of the summit.