The diamonds come from the Anglo-Australian firm's Argyle mine -- where more than 90 percent of the world's pink and red jewels are produced each year.
"This year, we probably have the most valuable tender ever," Rio Tinto diamonds and minerals chief executive Alan Davies told AFP of the annual sale.
"So we've got a number of fancy reds and the colour and the clarity this year is truly unique.
"They are so rare that all of the pinks you can have in the palm of your hand and all the reds you can count on one hand, so they truly are in the category of luxury collection."
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Rio said this year's selection, which weighs a total of 44.14 carats, had some of the "most vivid" pink and red diamonds ever unearthed from the mine.
The jewels are around 1.6 billion years old and routinely fetch USD 1-2 million a carat. As a basic rule of thumb, pink and red diamonds are worth about 50 times more than white diamonds.
Davies said there was worldwide interest in the diamonds -- which will go from Sydney to Hong Kong, New York and Perth before the bidding process closes on October 21 -- as they are viewed, like artwork, as collectibles.
"We've seen growth in value of more than 10 percent a year for more than 12 years, and we expect that to continue."
It is not known how the diamonds acquired their pink or red tinge but it is thought to come from a molecular structure distortion as the jewel forms in the earth's crust or makes its way to the surface.