The rouble firmed 0.6pc on the day against the U.S. dollar to touch 63.91 for the first time since April 24, and was 0.8pc stronger at 71.61 versus the euro.
The rouble's move comes after the finance ministry said it would auction two series of OFZ treasury bonds on Wednesday, setting the overall amount on offer at 25.3 billion roubles ($395 million).
Demand for OFZ treasury bonds buttressed the Russian currency in recent months.
"Quantitative easing by the European Central Bank and the prospect of the U.S. Fed cutting rates will prompt Western demand for emerging market assets, including for OFZ bonds," said a trader at a major Russian bank.
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. Yields of Russia's benchmark 10-year OFZ bonds dropped to 7.59pc on Tuesday, their lowest since July 2018, moving inversely with their prices.
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 probably increase demand for emerging market currencies as investors look for higher-yielding assets.
The head of the European Central Bank on Tuesday also raised the possibility of new rate cuts or asset purchases if euro zone inflation does not head back to its target.
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.
Russian stock indexes were up.
The dollar-denominated RTS index was up 1pc at 1,353 points, while the rouble-based MOEX Russian index was up 0.5pc at 2,748 points.