China's efforts to contain the outbreak of a new strain of the coronavirus also lifted appetite for riskier assets.
Russia's new government, tasked with boosting sluggish economic growth and attracting investment, was approved by President Vladimir Putin on Tuesday, ending investor uncertainty surrounding the cabinet makeup.
The rouble was not expected to react further to the new cabinet.
At 0757 GMT, the rouble was 0.1pc stronger against both the dollar and the euro at 61.82 and 68.53 respectively.
The rouble was hit this week by low risk appetite, sparked by concerns over a new strain of the coronavirus emerging in China, which has so far killed nine people.
However, Beijing's approach to the outbreak has helped temper some fears of a global pandemic.
The Russian currency is also expected to receive a boost from two OFZ treasury bond auctions later on Wednesday.
Demand for these bonds, which are auctioned weekly by the finance ministry, serves as a gauge of global market sentiment toward Russian assets.
Russian tax payments due in the second half of the month have also prompted export-focused companies to convert foreign currency revenues to meet local liabilities, protecting the rouble from further depreciation.
Russian stock indexes rose slightly.
The dollar-denominated RTS index was up 0.1pc at 1,636.3 points. The rouble-based MOEX Russian index was also 0.1pc higher at 3,212.3 points, hovering near a record high hit on Monday.
Brent crude oil, a global benchmark for Russia's main export, was down 0.6pc at $64.21 a barrel as of 0752 GMT.