The oil producer group, known as OPEC+, agreed on Sunday to reduce output by 9.7 million barrels per day (bpd) for May and June after four days of talks and following pressure from US President Donald Trump to arrest the price decline.
At 0740 GMT the rouble was up 0.3pc against the dollar at 73.51, moving away from a four-year low of 81.97 hit in mid-March.
Versus the euro, the rouble was 0.3pc up at 80.53 .
The OPEC+ deal, designed to reduce global oil output by about 20pc, may yet be insufficient to drive oil prices higher, given coronavirus-related demand destructruction amid travel restrictions and lockdowns worldwide.
Oil crude futures "pointed to persisting concerns that the cuts might be insufficient to stem the supply glut," VTB Capital said.
Brent crude oil, a global benchmark for Russia's main export, was up 0.3pc at $31.56 a barrel.
The rouble continues to gain support from the central bank, which has been selling foreign currency from state reserves since March. Last Thursday it sold 13 billion roubles ($172 million) of foreign currency, its data showed on Monday.
Russian stock indexes were weaker as coronavirus cases continue to rise, denting hopes that the lockdown imposed in many regions of the country will soon be lifted.
Deputy Prime Minister Tatiana Golikova said on Sunday that Russia will not defeat the coronavirus in time for Moscow's May 9 annual military parade to celebrate victory in World War Two.
The dollar-denominated RTS index shed 1.1pc to 1,128.8 points while the rouble-based MOEX Russian index was 1.7pc down at 2,631.1 points after rising since early April.