(Updates with rouble gains) MOSCOW, Oct 14 (Reuters) - The Russian rouble firmed against the dollar on Thursday to levels last seen in late July 2020, while a recovery in oil prices helped the benchmark MOEX stock index hit a record high. At 1304 GMT, the rouble was 0.6% stronger against the dollar at 71.54, having hit its strongest level since July 27, 2020 at 71.5150. Against the euro, the rouble also gained 0.6% to 83.01 . “The currency has performed well and we remain constructive in the medium term,” Morgan Stanley analysts said of the rouble against the euro, although they added they had decided to close a short euro-rouble position. Russian assets got a boost from prices for oil, the country’s main export, that rose after the International Energy Agency said record natural gas prices would boost demand for oil and Saudi Arabia dismissed calls for additional supply from the OPEC+ group of producers. Brent crude, a global benchmark, was up 1.1% at $84.09. Higher gas prices could help the rouble average 68.3 against the dollar next year, 2.5% stronger than previously thought, according to Sberbank CIB calculations. The rouble is likely to see extra support from higher interest rates at home as the central bank is expected to tighten monetary policy after annual inflation accelerated to 7.63%, a level last seen in February 2016. The market expects the central bank to raise its key rate from 6.75% by at least 25 basis points at its next board meeting on Oct. 22. Russian stock indexes were up. The rouble-based MOEX Russian index hit a record high of 4,292.689, before trimming gains to trade at 4,286.7, up 1% on the day. The dollar-denominated RTS index rose 1.38 to 1,887.9. For Russian equities guide see For Russian treasury bonds see Reporting by Andrey Ostroukh Editing by Subhranshu Sahu and Mark Potter Our Standards: The Thomson Reuters Trust Principles.