By 1029 GMT, the rouble had fallen 0.3% against the euro to 89.92 EURRUBTN=MCX, having earlier hit 90.40, its lowest mark since February 2016.
Versus the dollar, the rouble slid to just shy of its weakest since April 22, losing 0.7% to trade at 76.27 RUBUTSTN=MCX.
Oil prices fell on Monday because of the potential resumption of output from Libya. A global increase in coronavirus cases also added to worries about global oil demand, but a tropical storm heading for the Gulf of Mexico limited losses. O/R
Brent crude oil LCOc1, a global benchmark for Russia's main export, was down 2% at $42.29 a barrel.
"Russian stock indices and the rouble will likely decline this morning due to declining risk appetite from abroad," said Veles Capital analyst Elena Kozhukhova.
Geopolitical risks related to the political crisis in neighbouring Belarus and the suspected poisoning of Kremlin critic Alexei Navalny have weighed on Russian assets in recent weeks.
Month-end tax payments that usually lead export-focused companies to convert foreign currency revenues to meet local liabilities could support the rouble as they peak later this week, analysts said.
Alexei Antonov, an analyst at Alor brokerage, said the rouble would attempt to strengthen on Monday but would remain above 75 against the dollar.
Russian stock indexes were trading lower.
The dollar-denominated RTS index .IRTS was down 2.6% to 1,196.2 points. The rouble-based MOEX Russian index .IMOEX was 1.9% lower at 2,896.1 points.
For Russian equities guide see RU/EQUITY
For Russian treasury bonds see 0#RUTSY=MM
(Reporting by Gabrielle Tétrault-Farber and Alexander Marrow; Editing by Kirsten Donovan and Hugh Lawson)
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