By 0741 GMT, the rouble was 0.1pc up against the dollar at 63.73 and was slightly down versus the euro at 70.51.
The rouble is likely to be sensitive this week to comments by central bankers, with rate decisions expected from the US Federal Reserve on Wednesday, the European Central Bank on Thursday and Russia's central bank on Friday.
Maxim Korovin, a strategist at VTB Capital, said this Friday's central bank meeting is the "focal point" for Russia's money market.
Monday's meeting between Putin and Zelenskiy is the first between the heads of state of Russia and Ukraine in more than three years and will be overseen by French and German leaders, although diplomats said prospects for peace remain bleak.
Brent crude oil, a global benchmark for Russia's main export, was down 0.4pc at $64.1 a barrel.
Following a decision by the OPEC+ group of oil producers to commit to some of the sectors deepest output cuts in a decade, seeking to support prices, Brent crude reached a 10-week high, giving further support to the Russian currency.
Russian stock indexes were up.
The dollar-denominated RTS index rose 0.3pc to 1,452.2.
The rouble-based MOEX Russian index gained 0.3pc to 2,937.7.