At 0944 GMT, the rouble had shed 0.6pc of its value against the dollar to 79.39, moving closer to the 81.97 hit earlier this month, its weakest since early 2016.
The rouble has lost more than 20pc of its value so far this year, becoming one of the worst-performing currencies against the dollar.
Against the euro, the rouble lost 0.5pc to trade at 88.21 versus the euro, closing in on a four-year low of 89.60 it touched in mid-March.
The Russian currency is facing downside pressure as the economy slows. Moscow announced a partial lockdown, ordering residents to stay at home from Monday, in the toughest move yet to slow the spread of coronavirus after the number of official cases in the Russian capital passed 1,000.
The rouble also came under increased pressure as crude oil benchmarks fell on Monday. Brent dropped to its lowest in nearly 18 years, as fears grew over the coronavirus pandemic eroding demand and the Saudi Arabia-Russia price war threatened to overload the market.
Oil prices are falling amid concern that "Russia and Saudi Arabia will open their taps when the current agreement expires 1 April, while demand is threatened by intensifying measures to stem COVID-19", BCS Brokerage said.
The combination of oil prices dropping below $25 per barrel and "the very strict measures introduced by the city of Moscow will now all but ensure that the economy will indeed see negative growth in 2020," Citi analysts said.
Before the March sell-off, when the rouble traded at around 63-65 to the dollar, the Russian economy was expected to grow around 2pc this year.
Losses in the rouble were partly capped by the central bank's selling around $167 million in its first FX interventions since early 2015.
The central bank's actions, however, were not enough to offset the drop in Brent crude oil, a global benchmark for Russia's main export, which fell 8pc to $22.94 a barrel, putting pressure on Russian stocks.
The dollar-denominated RTS index was down 0.3pc to 950.1 points. The rouble-based MOEX Russian index was 0.1pc lower at 2,398.1 points.
Shares in Russia's oil major Rosneft outperformed stock indexes in early trade but soon slid 1pc on the day as the market priced in the company's decision to terminate operations in Venezuela.