At 0716 GMT, gas giant Gazprom's shares were down 6.9%, extending heavy losses from the previous session after it decided not to pay dividends on last year's results for the first time in more than two decades.
Meanwhile, shares in oil major Rosneft, which approved 2021 dividend payments after Thursday's closing bell, were gaining ground, up 4.6%.
"There are few reasons for optimism in the Russian market," said Otkritie Research in a note.
The commodity sectors of the market will be under pressure and the rouble may shed some ground before the weekend, Otkritie said.
The rouble was 2.7% weaker against the dollar at 52.84 and had lost 2.2% to trade at 54.85 versus the euro.
The rouble has become the world's best-performing currency this year, boosted by measures taken to shield Russia's financial system from Western sanctions imposed after Moscow sent troops into Ukraine on Feb. 24.
The measures have included restrictions on Russian households withdrawing foreign currency savings.
The strong rouble has raised concerns among officials and export-focused companies because it dents Russia's income from selling commodities and other goods abroad for dollars and euros.
Russian stock indexes were falling, extending Thursday's losses.
The dollar-denominated RTS index was down 2.7% to 1,309.4 points. The rouble-based MOEX Russian index was 0.3% lower at 2,198.3 points.
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(Reporting by Reuters; Editing by Gareth Jones)