At 0727 GMT, the rouble firmed 0.3% to 75.73 against the dollar after hitting 75.4525, its strongest since March 31.
Biden called on Putin on Tuesday to reduce tensions stirred by a Russian military build-up on Ukraine’s border and proposed a summit of the estranged leaders to tackle a raft of disputes.
The market took Biden’s proposal to meet Putin “as a sign of a de-escalation of the recently increased tensions over the situation in eastern Ukraine,” VTB Capital said.
The rouble is likely to trade within a range of 75.30-76.40 in the coming days if the geopolitical situation remains calm, VTB Capital said, adding that its USDRUB model suggests there is more upside room for the Russian currency.
The rouble decoupled recently from moves in other emerging markets as well as in the price of crude oil, Russia’s key export, as it was hammered by fears about the situation in Ukraine.
Two U.S. warships are due to arrive in the Black Sea this week in response to what U.S. and NATO officials say is the largest massing of Russian forces - with thousands of combat-ready troops - since Moscow seized Crimea from Ukraine.
Versus the euro, the rouble was up 0.1% at 90.65 after hitting 90.27, its strongest since April 6.
Brent crude oil, a global benchmark for Russia’s main export, climbed 1% higher to $64.27 a barrel, buttressing Russian stock indexes.
The dollar-denominated RTS index rose 1.7% to 1,482.9 points. The rouble-based MOEX Russian index was 1.2% higher at 3,566.8 points, moving towards an all-time high of 3,602.18 it touched in mid-March.
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For Russian treasury bonds see (Reporting by Andrey Ostroukh; Editing by Toby Chopra)