Sept 26 (Reuters) - The Russian rouble steadied near 96 to the dollar on Tuesday, trading in a narrow band, supported by upcoming tax payments and high oil prices.

At 0710 GMT, the rouble was 0.2% stronger against the dollar at 96.10 and had gained 0.3% to trade at 101.69 versus the euro. It had firmed 0.1% against the yuan to 13.13.

Month-end tax payments, that usually see exporters convert foreign currency revenues to pay local liabilities, support the rouble, but the currency can slide early on in the month once the period has passed.

The rouble has also now lost the temporary support of higher sales of foreign currency than usual by the central bank, which was selling around 21.4 billion roubles of yuan a day until the start of this week.

"At the end of the week, when the tax period ends, there is a high likelihood of the resumption of the national currency's smooth devaluation," said Alor Broker's Alexei Antonov.

Brent crude oil, a global benchmark for Russia's main export, was down 1.1% at $92.23 a barrel.

Russian stock indexes were lower.

The dollar-denominated RTS index was down 0.5% to 992.5 points. The rouble-based MOEX Russian index was 0.6% lower at 3,028.8 points.

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(Reporting by Alexander Marrow; Editing by Bernadette Baum)