At 0740 GMT the rouble was 0.2pc weaker against the dollar at 63.43 and had lost 0.1pc to trade at 71.48 versus the euro.
The rouble has come under increased pressure this month as shareholders who receive dividends tend to convert the roubles they get into other currencies, such as the dollar or the euro.
The central bank said last month that dividend payments would be 43pc higher between May and August in comparison with the same period last year.
The Russian currency is also no longer receiving support from monthly tax payments, which ended late last month.
These tax payments often prompt export-focused companies to convert their dollars to meet local duties.
But analysts do not expect the rouble to sharply weaken in the near future.
"The weakening of the rouble is still very moderate because banks have large reserves of foreign currency liquidity," said Denis Poryvay, an analyst at Raiffeisenbank in Moscow.
"Strong movements are unlikely until September."
Trading volumes are likely to be lower on Thursday as the United States observes a public holiday.
"The Russian market is likely to remain in a holding pattern, as there are no evident catalysts and global markets are struggling to find direction," Alfa Bank said in a note.
Russia's Central Bank Governor Elvira Nabiullina said on Thursday that the country needed to improve its investment climate for the economy to grow.
Oil prices, which usually buttress the Russian currency, fell on Thursday because of a smaller-than-expected decline in US crude stockpiles and concerns about the global economy.
Russian stock indexes were stable.
The dollar-denominated RTS index was unchanged at 1,402 points, while the rouble-based MOEX Russian index was stable at 2,822 points.