The rouble opened 0.4% stronger at 63.51 to the dollar, its strongest since August 2018, and was unchanged against the euro at 71.64.
The prospect of a key rate cut by the U.S. Federal Reserve would increase demand for emerging market currencies as investors look for higher-yielding assets.
The rouble this week hovered around two-month highs because of strong demand for OFZ treasury bonds, which serves as a gauge of global market sentiment toward Russian assets.
Demand for these bonds has soared this year after months of uncertainty surrounding possible new U.S. sanctions on holdings of Russian debt.
Oil prices, which often buttress the Russian currency, rose on Thursday on signs of improving demand in the United States, while OPEC and other producers finally agreed to a date for a meeting to discuss output cuts.
"The combination of factors that has emerged in the past few months is unique: a strong rouble that reacts little to fluctuations in oil prices, expectations of an easing policy from the Fed, heightened confidence that the Russian central bank will further cut rates and the absence of negative geopolitical factors," Rosbank said in a note.
The Russian central bank last week cut its key interest rate for the first time since March 2018, signalling that it could pursue a monetary easing policy to tackle slowing economic activity.
Russian stock indexes on were also up on Thursday.
The dollar-denominated RTS index was up 1% to 1,374 points, while the rouble-based MOEX Russian index was 0.4% higher at 2,771 points.