"The emerging and developing economies must have a greater voice and representation in international financial institutions," a joint communique said.
"We also believe that there is a strong need for a stable, predictable and more diversified international monetary system," it said.
Medvedev's comments that "the existing set of reserve currencies, including the US dollar, have failed to perform their functions" contributed to the dollar's slide across the board on Tuesday.
China, which holds nearly $2 trillion in foreign currency reserves, suggested in March that the dollar could be replaced as the world's main reserve currency, but it was silent on Tuesday, suggesting that there is little unity on any potential challenge to the dollar.
And Medvedev's chief economic aide, Arkady Dvorkovich, emphasised that Moscow did not want to see a sudden plunge in the dollar's value.
"There is an understanding that the last thing we need now is turmoil on financial markets," Dvorkovich said.
"No one wants to ruin the dollar, including us."
The Bric term was coined by Goldman Sachs economist Jim O'Neill in 2001 to describe the growing power of emerging market economies.
Tuesday's summit was an attempt to give the grouping a bigger political voice. The four nations account for 15 per cent of the $60.7 trillion global economy.
Goldman Sachs has predicted that in 20 years time they could together dwarf the G7 group of industrial nations and that China will overtake the US as world's largest economy.