The rouble shed 0.3% to 65.37 versus the dollar as of 0752 GMT, down from this week's peak of 64.36 it hit on Monday.
Against the euro, the rouble eased 0.4% to 72.86 .
The rouble is falling along with oil prices, while inflows of foreign funds into Russian government bonds buttress the currency, said Artem Zaigrin, an economist at Citi in Moscow.
Foreign investors increased their holdings of Russian OFZ treasury bonds in May, bringing the non-residents' share among OFZ holders to 29.4% as of late May, the central bank said on Thursday.
Demand for OFZ bonds has supported the rouble in the past few months. It is considered a gauge of investor sentiment towards Russian assets.
Brent crude oil, a global benchmark for Russia's main export, was down 1.4% at $65.95 a barrel, having fallen from May's high of $73.40 as trade conflicts spread and U.S. crude output returned to record levels.
Russian stock indexes were down.
The dollar-denominated RTS index dropped 0.6% to 1,279.0 points. The rouble-based MOEX Russian index declined 0.3% to 2,652.7 points.