At 0800 GMT, the rouble was 0.1pc stronger against the dollar at 76.38, having briefly hit 76.05, its highest since March 18.
Still, the rouble remains one of the worst-performing currencies against the greenback so far this year, and is under pressure from the economic fallout of the coronavirus outbreak.
Against the euro, the rouble was little changed on the day at 82.62, far away from levels of around 70 seen before a sell-off that began in late February.
The market is still reacting to the largest-ever weekly percentage gains in oil prices last week, on hopes that OPEC and its allies would agree to cut crude supply worldwide by at least 10 million barrels per day.
But oil prices slipped on Monday after Saudi Arabia and Russia delayed a meeting to discuss output cuts to April 9.
Brent crude oil, a global benchmark for Russia's main export, was down 3pc at $33.06 a barrel.
"The rouble volatility will be high because of oil prices in the coming weeks, but its firming to 70-75 against the dollar in the second half of 2020 remains the base scenario," said Dmitry Dolgin, chief economist at ING in Moscow.
Nordea bank said it sees the rouble returning to 75 against the dollar and 82 versus the euro in April.
The Russian central bank is supporting the rouble on a daily basis by selling foreign currency in its first interventions since early 2015.
Last week, the bank increased its daily sales to around 15.7 billion roubles ($205 million) worth of FX.
Russian stock indexes were up after days of heavy losses in March. The dollar-denominated RTS index was up 1.2pc to 1,062.7 points, while the rouble-based MOEX Russian index was 0.4pc higher at 2,582.8 points.