At 0803 GMT, the rouble was 0.2 percent weaker against the dollar against at 62.94 and eased 0.2 percent to trade at 75.12 versus the euro.
The rouble came under pressure from the finance ministry that said on Monday it would increase its daily purchases of FX for state reserves because of extra revenues from oil and gas exports.
"An increase in the (finance) ministry's activity on the currency market will become an extra negative factor for the rouble amid lower current account and (ongoing) foreign debt repayments," analysts at Rosbank said in a note.
The rouble also remained under pressure from uncertainty over the new government that should be appointed later this month.
First candidates for the new cabinet were proposed on Monday shortly after the inauguration of President Vladimir Putin.
"Investors will digest the list of Putin's nominees for the Cabinet of Ministers and his decree on national goals," analysts at BCS brokerage said in a note.
Players' desire to minimise risks ahead of Russia's bank holiday on May 9 had a negative impact on Russian assets.
The dollar-denominated RTS index was down 1.22 percent to 1,142 point, while its rouble-based peer MOEX was 0.64 percent lower at 2,282 points.
Still, oil prices remained supportive for Russian assets. Brent crude oil futures, a global benchmark for Russia's main export, were down 1.3 percent at $75.2 a barrel, hovering near highest since 2014 of $76.34 they hit on Monday.