With their already limited cash holdings of hard currency, Russian banks have few options for investing foreign currencies because of capital controls in Russia and the risk of funds abroad being frozen as a result of Western sanctions, causing some to introduce fees.

"The minimum sum for SWIFT transfers will be $20,000," Tinkoff said on its Telegram channel. "We are forced to introduce temporary restrictions due to the increased number of checks from western partners and the lower volume of payments processed for clients of Russian banks."

Those changes came into effect on Thursday. The bank had said that it would not impose commission on SWIFT transfers until after June 30.

Tinkoff said a 1% service fee it plans to deduct monthly on accounts in dollars, euros, pounds and Swiss francs, starting from June 23, would now apply on accounts with over 10,000 units, rather than 1,000.

The central bank said on Tuesday that service fees for bank accounts in foreign currency, introduced by some Russian banks, were unacceptable.

(Reporting by Reuters; Editing by Alexandra Hudson)