The rouble was 0.7 percent stronger at 61.14 versus the dollar as of 0726 GMT, heading towards levels of 57-58 it was at in early April before the United States imposed the latest set of sanctions on Moscow.
Against the euro, the rouble was 0.6 percent stronger at 72.14 after briefly touching 71.95, a level last seen on April 9.
The rouble has outperformed many other emerging market currencies so far this week, gaining support from tax payments that usually prompt export-focused companies convert their dollar revenues to meet local duties.
From the technical point of view, the rouble's firming beyond the 61.5 mark against the dollar might have triggered stop-loss orders that could pave the road for further gains "especially in light of the looming tax payments," VTB Capital said in a note.
"However, at current valuations the rouble looks fundamentally fair to us, given the level of oil prices and general risk sentiment."
Risk sentiment remained under pressure amid tensions between Moscow and the West as final details of Russia's possible retaliation to the latest US sanctions have not been revealed yet.
Brent crude oil, a global benchmark for Russia's main export, supported Russian assets by adding 0.7 percent to 79.77 a barrel.
The dollar-denominated RTS index rose 0.6 percent to 1,198.4 points, while its rouble-based peer MOEX was 0.2 percent lower at 2,328.8 points, pressured by the firming rouble.
Shares in Sberbank outperformed the broader market, gaining 0.2 percent on the day, after Russia's largest lender said it has agreed to sell its Turkish business, Denizbank, to Dubai's biggest lender Emirates NBD for $3.2 billion.