The company said in a statement the dividends will be reinvested to finance the group's Russian operations, "including its exploration, production, refining and marketing activities".
Analysts say the extra cash could also be handy for parent BP as it struggles to cover costs related to the worst oil spill in U.S. history, and help TNK-BP in its pursuit of some BP assets being disposed of in a $30 billion sale.
"Basically, the main shareholders are receiving cash that they can then use to buy assets from the parent company, and BP is in need of high dividend payouts now more than ever," said Denis Borisov, an oil analyst at The Bank of Moscow.
TNK-BP, half-owned by four Russia-connected billionaires, has its eye on BP assets in Vietnam, Venezuela and Algeria.
This month, BP's new Chief Executive Robert Dudley said it may sell its main Vietnam assets, worth around $1 billion, to TNK-BP without inviting other parties to bid.
Analysts also say TNK-BP's large dividends will help one of its shareholders, the oligarch Mikhail Fridman's Alfa Group, pay down debt related to its main assets -- Russian telecoms operator Vimpelcom and the retailer X5.
"It is possible that Alfa needs the money to pay debt secured against a range of its assets," said Evgeny Golosnoi, an oil analyst at Troika Dialog.
The company has not announced its third-quarter results, but the proposed payout is about 70 percent more than its first-half net income of $2.43 billion.
Last year TNK-BP paid 7.41 roubles per share for the first nine months, a total of 114.4 billion roubles. Dividends for the full year in 2009 totalled $4.93 billion -- nearly the company's entire net income.
TNK-BP declined to comment on the reason behind the rise in the proposed dividend payments this year.