At 0736 GMT, the rouble was 0.03 percent stronger against the dollar at 62.05 and had gained 0.12 percent to trade at 72.52 versus the euro.
The finance ministry is expected to increase state purchases of dollars and other foreign currency to their highest since it started replenishing its reserve fund in early 2017.
The finance ministry is set to publish the FX purchasing plan at 0900 GMT.
The rouble, however, retains support from prices for oil, Russia's main export. Brent crude oil, a global benchmark, was up 0.41 percent at $75.59 a barrel.
The rouble was also on track to receive some support from the central bank that the market expects to postpone rate cuts and hold the key rate at 7.25 percent at its board meeting on June 15.
Governor Elvira Nabiullina confirmed the market expectations on Monday, saying rising petrol prices were a threat for inflationary expectations.
Artem Zvonarev, a trader with VTB Capital, said it seemed the market was slowly switching to a "summer regime" as the rouble in the past few days lacked impetus to firm beyond a technical level of 61.70-61.80 versus the dollar.
Russian stock indexes were slightly up.
The dollar-denominated RTS index was up 0.1 percent to 1,181 points. The rouble-based MOEX Russian index was 0.12 percent higher at 2,326 points.