At 0807 GMT, the rouble was up 0.1pc against the dollar at 65.10 and had lost 0.1pc to trade at 71.49 versus the euro.
OFZ bond auctions, which take place on Wednesdays, usually prompt market players to convert foreign currency to buy the country's sovereign debt. Foreign investors hold around 30pc of OFZ bonds.
Analysts expect that further gains by the rouble and by stocks could be limited, amid fears over global trade and economic growth before U.S.-China trade talks, which are scheduled for Thursday.
"The rouble remains vulnerable due to uncertainty related to the outcome of trade talks," Nordea Bank analysts said in a note.
Brent crude oil, a global benchmark for Russia's main export, was steady at $58.2 a barrel.
The dollar-denominated RTS index was up 0.46pc to 1312.4 points.
The rouble-based MOEX Russian index was 0.17pc higher at 2712.5 points.