The rouble was 0.3pc stronger at 64.18 as of 1420 GMT after briefly firming to 64.13, just short of an eight-week high.
"We think USD/RUB will likely retest strong support at 64.2, but we do not expect a break below this level given the benign outlook for the greenback," Sberbank CIB said in a note.
The rouble extended gains it posted on Friday when the Bank of Russia trimmed the key rate to 7.50pc from 7.75pc, lowering the cost of lending for the first time since March 2018 and promising to deliver one or two more cuts later this year.
Dovish monetary policy decisions and expectations tend to support prices of Russian treasury bonds, known as OFZs, which are popular among foreign investors.
Demand for such bonds usually supports the rouble as market players convert foreign currency into roubles.
"The rouble just loves the doves and we see more flows into OFZs given the current rate and inflation outlook and a lack of news on new anti-Russia sanctions," Danske Bank said in a note.
The Finance Ministry will hold weekly OFZ bond auctions on Wednesday after a break last week due to a public holiday.
Investors will also keep an eye on President Vladimir Putin, who on Thursday hosts an annual TV phone-in with citizens that usually lasts several hours and covers issues from bad roads to foreign relations.
Versus the euro, the rouble was 0.1pc stronger at 72.12 .
Russian stock indexes were steady, pricing in swings in oil prices. Brent crude oil, a global benchmark for Russia's main export, was down 0.4pc at $61.76 a barrel.
The dollar-denominated RTS index rose 0.5pc to 1,347.2, while the rouble-based MOEX index gained 0.2pc to 2,745.1 points, below an all-time high of 2,772.06 hit on Friday.