The rouble hit 70.16 versus the greenback at the market opening, taking its year-to-date losses to 19 percent.
The weaker rouble, hit by new sanctions against Moscow and a sell-off in other emerging markets, is seen filtering into consumer prices and once again boosting inflation, which the central bank has just recently managed to rein in.
Kremlin economic aide Andrei Belousov said on Monday a possible rate increase would be "highly undesirable" after Prime Minister Dmitry Medvedev said late last week that lending rates in Russia should be lower.
Russia's central bank is independent and Nabiullina is viewed by markets and investors as a stable hand on the tiller.
The rouble's fall, however, is likely to be limited by Russian export-focused companies that usually use attractively high levels of foreign currency to convert their dollar or euro revenues into roubles for their needs at home, such as to pay taxes due in the second half of the month.
Russian stocks firmed on the back of an increase in oil prices, Russia's key export. Brent crude futures were up 0.94 percent at $77.57 per barrel.
For Russian equities guide see
For Russian treasury bonds see
(Reporting by Andrey Ostroukh; Editing by Emelia Sithole-Matarise)
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