At 0745 GMT, the rouble was 0.4% stronger against the dollar at 64.49 and had gained 0.4% to trade at 71.98 versus the euro.
Oil rose to multi-week highs on Monday after OPEC indicated it would probably maintain production cuts that have helped support prices this year.
Brent crude oil, a global benchmark for Russia's main export, was up 1.36% at $73.19 a barrel at 0720 GMT, supporting the Russian currency.
"The domestic market could face a dilemma: follow commodity prices or be alarmed by the growing pressure on China," said Andrei Kochetkov of Otkritie Brokerage.
Kirill Tremasov, a former economy ministry official and now head of research at Loko-Invest, said the situation on emerging markets remained gloomy.
"Since the start of May all the currencies of the largest developing countries have been down," he said. "There hasn't been such a decline since June last year."
But other analysts say the rouble still has room to grow due to expectations that the central bank will cut its key rate next month after economic growth in Russia slowed to its weakest level since late 2017.
"The rouble could still grow because the market is awaiting a rate cut by the central bank, including because of the growing demand for OFZ bonds," said Alexei Antonov, an analyst at Alor Brokerage, referring to bonds that are auctioned weekly by the finance ministry.
Demand for OFZ bonds serves as a gauge for global market sentiment toward Russian assets.
Russian stock indexes were up.
The dollar-denominated RTS index was up 0.5% at 1,260.60 points. The rouble-based MOEX Russian index was 0.1% higher at 2,581.34 points.