GENEVA—The catalog listing was “an important and rare vivid blue diamond ring,” and it went for a price to match: 10,498,500 Swiss francs ($9,501,000), including the buyer’s premium, at a Sotheby’s auction here Tuesday night.

The estimate for the 7.03-carat diamond was 6,850,000–10,000,000 francs ($6,199,000–9,048,000).

According to the Web site swissinfo.ch, the stone was sold to one of two competing telephone bidders after a 15-minute battle. The site added that the price per carat was the highest ever paid for a gemstone at auction.

Sotheby’s said the diamond was flawless. It was cut from a 26.58-carat rough stone unearthed last year at Petra Diamond's Cullinan mine, near Pretoria, South Africa. The winning bidder, who has so far chosen to remain anonymous, will get to name the stone.