By 0727 GMT, the rouble had gained 0.7% to trade at 61.67 versus the euro, earlier clipping a one-week high of 61.60. It was 0.3% stronger against the dollar at 60.72.
The rouble is the world's best-performing currency this year thanks to capital controls and is expected to find more support soon from month-end tax payments that usually prompt export-focused companies to convert part of their foreign currency revenues.
The rouble is likely to trade in the range of 60 to 62 against the dollar until exporters become more active in terms of tax payments, Promsvyazbank analysts said in a note.
Rouble volatility has declined recently after wild swings carried it to a record low of 121.53 against the dollar on the Moscow Exchange in March, days after Russia sent tens of thousands of troops into Ukraine on Feb. 24, before rallying in June to a seven-year peak of 50.01.
Trading curbs on Russian markets are gradually easing. Moscow Exchange has permitted investors from "friendly" jurisdictions, or those which had not imposed sanctions on Russia, to start trading on the derivatives market after an almost six-month hiatus.
That ruling does not apply to the main stock market, but since Monday, Moscow Exchange has allowed non-residents from "friendly" countries to trade bonds.
"A positive factor now is the fact that with the return of non-resident investors to the debt market, there was no selling overhang," said Alfa Capital.
Russian stock indexes were climbing.
The dollar-denominated RTS index was up 1% to 1,153.1 points at its highest since late July. The rouble-based MOEX Russian index was 0.7% higher at 2,222.9 points, a more than five-week high.
(Reporting by Alexander Marrow; Editing by Clarence Fernandez)
