(Reuters) - The Russian rouble surged to new multi-week highs on Friday while stocks fell in volatile trade as Moscow mobilises some 300,000 extra troops for the conflict in Ukraine.

Despite President Vladimir Putin's mobilisation order, the rouble hit its highest level versus the U.S. dollar since Aug. 19 this week and its strongest against the euro since July 27.

After initially falling against the U.S. dollar, the rouble recovered and was up 2% against the greenback at 57.71 by 1021 GMT. Against the euro, the rouble was 2.5% stronger at 56.18.

Currency controls and month-end tax payments which see Russia's exporters convert their foreign currency earnings into roubles to make payments to the treasury are providing a boost to the rouble despite the geopolitical headwinds, analysts say.

Stocks were deep in the red as markets remain jittery over how Russia's mobilisation drive will affect the conflict. The dollar-denominated RTS index dropped 1.8% to 1,153.5 points. The rouble-based MOEX Russian index was 3.6% weaker at 2,112.4 points.

Russian shares have seen heightened volatility all week in response to the mobilisation order and as Moscow stages referendums in four regions of Ukraine on joining Russia.

The new moves from Moscow have raised the prospect of further economic sanctions from the West, with the European Union saying it will discuss a new package of penalties.

After surging in Thursday's session on news it had enough free cash flow to pay interim dividends, shares in Gazprom fell back in line with the wider market on Friday, down 2.6% in rouble terms.

"Today the Russian market is dominated by negative sentiment ... the Friday factor seems to be stronger than usual as market players are not risking keeping their long positions over the weekend," said Zarina Saidova, an analyst at Moscow-based Finam investment firm.

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(Editing by Alexander Smith, Kirsten Donovan)