MOSCOW, Jan 20 (Reuters) - The Russian rouble fell from near 76 versus the dollar on Thursday, but clung onto some gains after recovering in the previous session, while Russian stocks climbed with investors still focused on geopolitics.

The Kremlin on Wednesday said measures were being taken to maintain economic stability after several sessions of volatility and sharp losses for Russian assets, buffeted by Western fears over a Russian troop build up at Ukraine's border.

At 0728 GMT, the rouble was 0.5% weaker against the dollar at 76.53 and had lost 0.5% to trade at 86.90 versus the euro.

"The local market will remain subject to geopolitical tossing and turning – despite attractive fundamentals, geopolitics clouds all," said BCS Global Markets in a note.

U.S. President Joe Biden predicted on Wednesday that Russia would make a move on Ukraine, saying Russia would pay dearly for a full-scale invasion, but suggesting there could be a lower cost for a "minor incursion."

Russia says it is concerned about NATO's expansion and has repeatedly denied planning to invade Ukraine.

But the Kremlin has said tension around Ukraine was increasing. U.S. Secretary of State Antony Blinken and Russian Foreign Minister Sergei Lavrov are due to hold talks on Friday.

Brent crude oil, a global benchmark for Russia's main export, was down 0.3% at $88.14 a barrel, but hovering near its highest level since late 2014, helping Russian stock indexes surge higher.

The dollar-denominated RTS index was up 1% to 1,428.9 points. The rouble-based MOEX Russian index was 0.8% higher at 3,464.5 points.

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(Reporting by Alexander Marrow Editing by Mark Potter)