(Recasts with details from central bank statement, adds response from OTP, new throughout)

BUDAPEST, May 29 (Reuters) - Hungary's central bank told OTP Bank on Wednesday to curb its Russian exposure further and take several precautionary measures that the Hungarian financial supervisor will monitor on an ongoing basis.

Central Europe's largest independent lender has gradually decreased its footprint in Russia since Moscow's February 2022 invasion of neighbouring Ukraine, though its exposure is still third-highest among European banks, behind Raiffeisen Bank and UniCredit, based on a tally by Morningstar DBRS.

Hungary's central bank said risks may arise regarding OTP's Russian activity and payment transactions due to Western sanctions imposed on Russia as well as differences between Russian and European Union rules on the prevention of money laundering, the financing of terrorism and compliance measures.

"The compliance department of the parent bank should draw up and continuously update a set of criteria approved by OTP Bank's top management regarding international payment transactions deemed as carrying an acceptable level of risk for the group," the central bank said.

The central bank also said OTP should wind down its corporate loan stock in Russia, keep its retail loan stock stable and reduce its stock of retail deposits.

"The measures can contribute to the banking group's continued stable, profitable and reliable operation," the central bank said. It also told OTP to draw up an action plan approved by its board of directors and report regularly on its implementation.

OTP said the fulfillment of the Hungarian central bank's recommendations would not have an impact on its group-level management expectations for 2024.

"Based on data from the first quarter of 2024, the local credit market share of the Russian subsidiary of OTP Group is only 0.14%, and its share within the entire OTP Group is 4.2%based on total assets," the bank said in a statement.

OTP says its corporate loan stock in Russia fell by 85% since the start of 2022, while the size of its Russian branch network shrank by 39%.

"OTP Group has already significantly limited its international payment services from and to Russia," it said. "As part of this, for example, it has completely cancelled its services related to customer transactions in U.S. dollars involving Russia." (Reporting by Gergely Szakacs in Budapest Writing by Anna Wlodarczak-Semczuk Editing by Timothy Heritage, Richard Chang and Matthew Lewis)