The term BRIC was coined by Goldman Sachs economist Jim O'Neill in 2001 to describe the rise of Brazil, Russia, India and China. The BRIC powers had their first summit in 2009 in Russia. South Africa joined in 2010.
"We expect BRICS will give us a positive response to the request we have made," foreign ministry spokesman Meles Alem told journalists, according to the state-run news agency ENA.
Ethiopia will continue to work with international institutions that can protect its interests, he said.
The horn of Africa nation has the second-largest population in Africa, but its economy ranks only 59th in the world according to the International Monetary Fund, and is less than half the size of the smallest BRICS member South Africa.
Last year Argentina, the world's 23rd-largest economy, said it had received China's formal support to join the group, which is seen as a powerful emerging-market alternative to the West.
South Africa said on Thursday it will host the next summit in August as planned, amid speculation it could be moved to a location where Russia's President Vladimir Putin would not be obliged to be arrested over war crimes accusations.
BRICS countries account for more than 40% of the world's population and about 26% of the global economy.