At 0710 GMT, the rouble was unchanged against the dollar at 64.29 and was 0.1% weaker at 72.25 versus the euro.

The U.S. Federal Reserve begins a two-day policy meeting on Tuesday and is expected to lay the groundwork for a rate cut later this year. This would most likely increase demand for emerging market currencies as investors look for higher- yielding assets.

The Russian central bank last week cut its key interest rate for the first time since March 2018, signalling it could pursue a  monetary easing policy to tackle slowing economic activity.

The rouble is also buttressed by investor expectations for strong demand for OFZ treasury bond at auctions due to be held on Wednesday.

Demand for the bonds, which were not auctioned last week because of a public holiday, serve as a gauge of global market interest in Russian assets and usually support the Russian currency.

"The rouble is preparing for OFZ auctions that did not take place last week," said Andrei Kochetkov, an analyst at Otkritie Brokerage. "There could be additional demand for rouble liquidity from exporters."

The rouble could test the 64 mark against the dollar in the short term because it is receiving support from month-end tax payments that prompt export-focused companies to convert foreign currency to meet local liabilities, Rosbank said in a note.

Russian stock indexes were mixed.

The dollar-denominated RTS index was down 0.1% at 1,339 points, while the rouble-based MOEX Russian index was steady at 2,732 points.