At 0735 GMT, the rouble was 0.3 percent stronger against the dollar at 62.48 and had gained 0.2 percent to trade at 70.09 versus the euro.
Brent crude oil, a global benchmark for Russia's main export, was up 1.3 percent at around $51.5 a barrel after a report that U.S. fuel inventories may have fallen for a fifth straight week.
The Russian currency is up around 0.5 percent against the dollar this week after hitting a 2016 high on Monday.
It has mainly been lifted by gains in oil, but also by the attractiveness of Russian assets for developed-market investors starved of high yields.
Russia's dollar-denominated RTS share index was down 0.5 percent to 995 points on Wednesday, while the rouble-based MICEX was 0.5 percent lower at 1,975 points.
The losses were attributed to a Bloomberg report on Tuesday which said the ECB would probably wind down its 80 billion euro ($90 billion) monthly bond purchases gradually before ending its quantitative easing programme.
Although the ECB denied its decision-making body had discussed reducing the pace of its monthly bond buying, the report sent ripples through global markets nervous about the prospects of reduced central bank stimulus.