At 1050 GMT, the rouble gained 1.9% to 58.97 against the euro, its strongest level since May 25..

Against the dollar, the rouble was unchanged at 56.81 close to multi-year peaks, supported by capital controls that Russia imposed in late February after sending tens of thousands of troops into Ukraine.

After the rouble became the world's best-performing http://fingfx.thomsonreuters.com/gfx/rngs/GLOBAL-CURRENCIES-PERFORMANCE/0100301V041/index.html currency, authorities eased capital controls and scrapped a requirement for export-focused companies to convert their foreign-currency revenues.

The central bank's decision to cut its key rate to the pre-crisis level of 9.5% last week should also ease upside pressure on the rouble.

The rouble strengthening dents incomes of exporters and Russia's budget but is beneficial for importers, making foreign goods and services cheaper. However, Russian imports have waned drastically due to unprecedented western sanctions and disrupted logistics chains.

Sberbank CIB analyst Yuri Popov said higher foreign exchange sales by exporters in order to meet domestic tax obligations were supporting the rouble on Tuesday. Hard currency savings have also "started losing their appeal as Russian banks introduced fees for servicing accounts in currencies of 'unfriendly' countries," Popov added in a research note.

The Moscow Exchange said on Tuesday it would suspend trading the Swiss Franc against the U.S. dollar and the rouble due to the sanctions Switzerland has imposed on Russia from June 10.

Russian stock indexes were up slightly after starting the day weaker.

The dollar-denominated RTS index was up 0.2% at 1,270.7 points, after slumping 2% in early morning trading. The rouble-based MOEX Russian index gained 0.3% to 2,292.5 points.

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(Reporting by Reuters, editing by Ed Osmond and Tomasz Janowski)