At 0730 GMT, the rouble was up 0.13 percent against the dollar at 64.80 and was unchanged at 73.04 versus the euro.
Oil prices rose to five-month highs on Tuesday, supporting the Russian currency and helping the MOEX stock index reach a record high on Tuesday.
Andrei Kochetkov, an analyst at Otkritie Brokerage, said the rouble had felt the effect of high oil prices and could continue to gain ahead of auctions for Russian treasury bonds.
"It's likely that investors are already preparing for the auction of OFZ treasury bonds and that the rouble will continue to strengthen," he said, referring to auctions by the finance ministry taking place on Wednesday.
Demand for OFZ bonds is a gauge of market sentiment towards Russian assets and usually supports the rouble if investors convert foreign currencies to take part in the auctions.
Analysts say that the rouble's gains along with oil will remain moderate given uncertainty regarding external conditions and investor attitudes towards emerging markets.
"In many respects the uncertainty regarding sanctions is not allowing the rouble to realise its potential," Mikhail Poddubsky of Promsvyazbank said in a note.
Russian stock indexes were up on Tuesday.
The rouble-based MOEX Russian index was 0.33 percent higher at 2,569.84 points, an all-time high. The dollar-denominated RTS index reached 1,249.42 points, its highest since April 2018.