At 0752 GMT, the rouble was 0.8 percent stronger against the dollar at 68.38, moving away from 69.13, its weakest level since mid-September hit on Friday.
Versus the euro, the rouble gained 0.5 percent to 77.84 versus.
"In the run-up to the Christmas and New Year holidays, risk-sentiment will still likely remain vulnerable," analysts at VTB Capital said in a note.
Brent crude dynamics will be the most important driver for the rouble, while month-end tax payments "will likely provide some breathing space for it from the local side," VTB Capital said.
Brent crude oil, a global benchmark for Russia's main export, rose 0.6 percent to $54.14 a barrel, up from this year's low of $52.79 touched on Friday.
Local month tax payments usually prompt export-focused companies convert their revenues on the market in order to meet local duties, which supports the rouble.
Russian stock indexes were down.
The dollar-denominated RTS index was 0.12 percent lower at 1,075.8 points, while the rouble-based MOEX Russian index shed 0.5 percent to 2,334.3 points.