At 0734 GMT, the rouble was 0.9pc stronger against the dollar at 78.88, trading near its weakest since late January 2016 of 81.97 hit last Thursday.
"We expect the US currency to move within a range of 78-80 roubles during this session," said Bogdan Zvarich, chief analyst at Promsvyazbank.
Against the euro, the rouble was 0.1pc stronger at 85.38 , well away from levels of around 70 seen a month ago before the latest sell-off.
The rouble's downside has been partially limited by the central bank, which started selling a limited amount of FX from its reserves this month in its first currency intervention since 2015.
On Friday, the central bank sold 13.3 billion roubles ($168.71 million) worth of FX, its data showed on Monday.
The FX selling, however, was not enough to reverse the rouble's weakening trend that is now threatening to hit the Russian economy.
The central bank last week kept rates unchanged, deciding not to cut rates to support economic activity as other central banks have done due to risks of higher inflation, fanned by a steep drop in the rouble.
The Russian economy now faces a mounting risk of recession as the government is preparing to revise its spending priorities amid low oil prices and stalling business activity due to the global coronavirus outbreak.
Month-end taxes in Russia should also cushion losses in the rouble for now as export-focused companies usually convert their FX revenues to meet local liabilities at the end of every month.
Brent crude oil, a global benchmark for Russia's main export, was up 3.6pc at $27.99 a barrel, propping up Russian markets as it bounced from 2020 lows.
The dollar-denominated RTS share index was up 6pc to 936.8 points. The rouble-based MOEX Russian index was 4.2pc higher at 2,345.2 points, away from its record high of 3,226.9 it high two months ago.