MOSCOW - The Russian rouble steadied on Monday near multi-year peaks, supported by capital controls, and may continue firming later this month due to month-end tax payments.

At 0758 GMT, the rouble eased 0.2% to 56.52 against the dollar and shed 0.5% to 59.18 against the euro , still hovering near its strongest level in nearly five years of 57.10 it hit in May.

The rouble, which became the world's best-performing currency this year, is steered by Russia's high proceeds from commodity exports and a sharp drop in imports along with a ban on households withdrawing their foreign currency savings.

Top policymakers used Russia's annual economic forum in St. Petersburg last week to highlight the rouble's recent strength. There are concerns this could weigh on the economy as it tips into recession amid harsh sanctions over what Moscow calls a "special military operation" in Ukraine.

First Deputy Prime Minister Andrei Belousov said the rouble was overvalued and industry would be more comfortable if it fell to between 70 to 80 against the U.S. dollar.

Still, this week the rouble could extend gains as companies will need to pay taxes, for which export-focused firms usually convert their dollar and euro revenues.

The dollar will consolidate within a range of 55.5-57.5 to the rouble during the day, Promsvyazbank analysts said in a note.

Russian stock indexes were mixed, lacking momentum.

The dollar-denominated RTS index slid 0.2% to 1,312.9 points. The rouble-based MOEX Russian index was 0.2% higher at 2,358.8 points.

(Reporting by Reuters Editing by Mark Heinrich)