Sept 19 (Reuters) - The Russian rouble strengthened on Tuesday towards 96 against the dollar, supported by high oil prices and the central bank's foreign currency sales, but was still struggling to pull away from the 100 threshold it crossed last month.

At 0806 GMT, the rouble was 0.4% stronger against the dollar at 96.17 and had gained 0.2% to trade at 102.89 versus the euro. It had lost 0.4% against the yuan to 13.16.

The Bank of Russia jacked up the cost of borrowing at a third meeting in succession on Friday in response to the weak rouble, which tumbled to a near 17-month low of 101.75 to the dollar in August. Rate increases appear to have only had a limited effect so far.

"For some time the devaluation impulse of the Russian currency has subsided, but it will definitely resume after some time if monetary authorities do not take tough steps, first of all, to limit the outflow of capital from the country," said Alor Broker's Alexei Antonov in a note.

President Vladimir Putin on Monday said the weakening rouble was obviously one of the main inflation drivers and expressed confidence that the government and central bank would make timely decisions to manage the issue.

Authorities are discussing whether to reintroduce stringent currency controls to support the rouble, but Central Bank Governor Elvira Nabiullina on Friday warned such steps were inefficient and would ultimately be circumvented.

The central bank sharply increased its foreign currency sales for a week starting on Sept. 14, seeking to compensate for the redemption of $3 billion worth of Russian Eurobonds on Sept. 16.

Brent crude oil, a global benchmark for Russia's main export, was up 0.5% at $94.92 a barrel.

Russian stock indexes fell.

The dollar-denominated RTS index was down 0.4% to 1,020.8 points. The rouble-based MOEX Russian index was 0.6% lower at 3,117.2 points.

Moscow-listed shares in gold and silver producer Polymetal leapt 10% at the market open before settling around 5% higher, as trading resumed after a break as the company re-domiciled from Jersey to Kazakhstan. (Reporting by Alexander Marrow; Editing by Kirsten Donovan)