And that means competing with the top tier — that is, brands such as Graff, De Beers and Chopard.

"We're concentrating on the very high end," said Leviev president and chief operating officer Thierry Chaunu, former president and chief executive officer of Chopard in the U.S. who is spearheading the brand's rollout.

"The air is obviously very thin at the top of the diamond trade," said Leviev, comparing diamond brands with art dealers. "Each [art dealer] specializes in different time periods, just as each jewelry brand tends to specialize in a specific style or diamond quality. We are different from everybody else by the wide range of extraordinary jewels we offer. We are the only independent diamond company that fully controls the entire life cycle of a diamond, from mining to cutting, polishing, marketing and retailing. It is this unsurpassed experience and knowledge that puts Leviev in a realm others only strive to reach. We can spend years creating a necklace of perfectly matched D-flawless diamonds. Exceptional diamond jewelry is our specialty."

François Curiel, chairman of Christie's Europe and head of jewelry for the auction house, said the global diamond market is about $60 billion and that the high-end retail diamond market is about $25 billion to $30 billion, leaving room for a few operators.

Nonetheless, the Madison Avenue opening is a bold move by a relatively little-known brand offering exorbitantly priced jewelry. Those in the diamond industry are familiar with the name, but Leviev is hardly a household name, even amongst the superrich.

Curiel said such icons in the jewelry world likely faced similar struggles for brand recognition: "When Harry Winston started and there was Van Cleef and Cartier [everyone probably thought], who was Harry Winston?"

And, over the past two years, Leviev's aggressive public relations campaign has nabbed several celebrity wearers, including Salma Hayek, Drew Barrymore, Ginnifer Goodwin and Jennifer Hudson, but Chaunu is cautious of rushing into anything.

"We're humble," he said. "We're not saying here that we are conquering the world. If there's one thing [Leviev] resents, it's attitude."