The rouble was 0.3 percent stronger at 66.36 as of 0721 GMT , hovering at levels seen in the three previous trading sessions.
Against the euro, the rouble was 0.2 percent weaker at 75.55 .
The market is watching tensions between Moscow and Kiev to see if they lead to more sanctions on Russia, which opened fire on Ukrainian navy boats and then seized the boats and their crew last month near Crimea, which Russia annexed in 2014.
Prices for oil, Russia's key exports, inched higher before a meeting of OPEC and its allies this week. Brent crude futures were 1.1 percent higher at $62.39 per barrel.
The Middle East-dominated Organization of the Petroleum Exporting Countries meets on Thursday in Vienna to discuss output policy. OPEC will also discuss policy with Russia.
The Russian Finance Ministry will announce details of its weekly auctions of OFZ treasury bonds. Demand for the bonds is a gauge of sentiment, given uncertainty about whether Washington will impose sanctions on holdings of Russian state debt.
VTB Capital analysts said the Finance Ministry could double its offering of OFZ bonds from last week to 20 billion roubles ($301 million) "given a strong recovery in the OFZ market in the last several sessions."
Russian stock indexes were down. The dollar-denominated RTS index slid 0.1 percent lower to 1,153.4 points, while the rouble-based MOEX Russian index was 0.4 percent lower at 2,430.6 points.