Islamic banks across six core markets of Qatar, Indonesia, Saudi Arabia, Malaysia, the United Arab Emirates and Turkey held $625 billion at the end of 2013 or 80 percent of the global Islamicfinance market, the report said. The figure was 95 percent when Bahrain, Pakistan and Kuwait are included. Estimates exclude Iran which has a distinct model for Islamic finance, which follows religious guidelines such as a ban on interest and on pure monetary speculation.

The report estimated the combined Islamic banking assets in the six core markets will reach $1.8 trillion by 2019, buoyed by growth which has been 1.9 times faster than that of conventional banks over the 2009-2013 period.

The six core markets now comprise 82 percent of the global industry, and this could rise even further, said Ashar Nazim, a partner at EY's global Islamic banking center.

"As the populous centers of Turkey and Malaysia gain momentum and Saudi banks continue their transformation to sharia compliance, we expect the market share to account for between 80 percent to 90 percent of the global market."

Beyond these markets, the industry is expected to make some gains in Egypt, Pakistan and North African countries such as Tunisia, Algeria and Morocco, Nazim added.

"However, in the absence of regulatory reforms and strong sovereign support, the pace of growth is likely to be moderate."

Islamic bank revenues are also underweight on trade finance and lending to medium-sized businesses, two core areas in fast-growing emerging markets. According to EY, 10 of the 25 high-value emerging markets are core Islamic finance markets.

"This is a once-in-15-year-opportunity to capture the share of this evolving trade market for younger Islamic banks," Nazim said.

Entry into such markets would allow Islamic banks to build much-needed scale, but many lack the expertise and risk appetite to venture abroad, which has in turn affected profitability.

Average return on equity for a sample of the top 20 Islamic banks was 11.9 percent over a five year period, compared to 14.5 percent for a sample of 20 conventional banks, the report said.

The top 20 Islamic banks were roughly a quarter the size of their conventional peers.