Russian state-owned diamond miner Alrosa, which starts a road-show for a share sale next week, said on Friday its third-quarter production rose 9 percent on improved operations at its mines in Russia's Far East.

Alrosa's offering of 16 percent more of its shares in Moscow this month could value the business at more than $10 billion. The company, the world's top diamond producer by output in carats, will be one of a handful of listed diamond miners.

Its third-quarter 2013 diamond production totalled 9.9 million carats, up from 9.1 million carats for the same period a year ago, the company said in a statement.

Production was boosted by the acquisition of Nizhne-Lenskoye, which mines diamonds from alluvial deposits in the Republic of Sakha (Yakutia), while the grade of diamonds in the ore of its Jubilee pipe improved and output from its Mir underground mine increased.

Alrosa's roots date back to the first Russian diamond mine, discovered in the 1950s.

It has been steadily growing its production and market share over the decades, overtaking Anglo American-owned De Beers in 2009 as the world's biggest diamond producer by volume, though it has yet to catch up in value terms.

Russia's federal and regional governments plan to sell 14 percent of Alrosa's shares this month, using the cash to bolster state finances. An additional 2 percent will be sold by an Alrosa subsidiary and these proceeds will be used to pay down debt.

Alrosa has a free float of 9 percent, according to the company, although bookrunners say this figure includes the 2 percent stake that Alrosa plans to sell, and its real free float is 7 percent. This is expected to rise to 23 percent after the deal.