MOSCOW, Nov 28 (Reuters) - The Russian rouble firmed on Tuesday, hovering close to a multi-month high, supported by exporters paying monthly taxes as the market assessed a central bank announcement that it would adjust its formula for currency interventions in the new year.

At 0801 GMT, the rouble was 0.2% stronger against the dollar at 88.59 and had gained 0.4% to trade at 96.92 versus the euro. It had firmed 0.2% against the yuan to 12.37.

The Bank of Russia said on Monday it would resume interventions in the domestic foreign exchange market from January, but using new methodology that analysts said would likely support the rouble.

The rouble has strengthened against the dollar for seven weeks in a row, rebounding from past 100 thanks to reduced capital outflows since President Vladimir Putin introduced capital controls in October.

The rouble may weaken in December, said Alor Broker's Alexei Antonov, as budget payments are finalised and demand for foreign currency from the population picks up ahead of Russia's long New Year holidays.

Month-end tax payments, due on Tuesday, which usually see exporters convert foreign currency revenues to pay local liabilities, have also been supporting the rouble, as have expectations of another interest rate increase.

The Bank of Russia, which meets on Dec. 15, raised rates to 15% in late October and has signalled that another increase may be needed.

"It is highly likely that in December the Bank of Russia will still be ready to make a tough step for neutralising inflation risks," said Alfa Bank analysts in a note, with inflation set to comfortably exceed the bank's 4% target.

Brent crude oil, a global benchmark for Russia's main export, was up 0.2% at $80.16 a barrel.

Russian stock indexes were lower.

The dollar-denominated RTS index was down 0.6% to 1,124.8 points. The rouble-based MOEX Russian index was 0.9% lower at 3,163.9 points.

Moscow-listed shares in SPB Exchange, Russia's second-largest bourse, were down 1.5%, not far from the record low hit in the previous session when it was forced to deny it had filed for bankruptcy, blaming fraudsters for rogue filings with a Russian court. (Reporting by Reuters; Writing by Alexander Marrow, Editing by Miral Fahmy)