Expectations of lower rates in the United States usually support emerging-market assets, including the Russian rouble and bonds.
The rouble was 0.4% stronger against the dollar at 66.32 by 0720 GMT and had gained 0.4% to trade at 73.56 versus the euro.
The U.S. Federal Reserve is set to release minutes from its meeting last month later on Wednesday, while Fed Chairman Jerome Powell will speak on Friday, when he is expected to give guidance on the possibility of a rate cut in September.
The rouble is also receiving a boost from a rise in the price of oil to above $60 a barrel, and upcoming month-end tax payments that prompt export-focused companies to convert foreign currency revenue to meet local liabilities.
The Russian currency could also be buttressed by the finance ministry's weekly auction of OFZ treasury bonds later on Wednesday. Demand for these bonds serve as a gauge for market sentiment toward Russian assets.
VTB Capital said in a note that the rouble was faring slightly better than other emerging market currencies because of non-residents' purchases of OFZs and increased selling of hard currency by exporters ahead of major tax payments.
Russian stock indexes were mixed on Wednesday.
The dollar-denominated RTS index was up 0.3% at 1,268 points, while the rouble-based MOEX Russian index was 0.1% lower at 2,669 points.