BRUSSELS, July 13 (Reuters) - The European Commission approved on Monday a €2 billion ($2.3 billion) capital injection by Hungary into the country's Magyar Fejlesztesi Bank, which comes as Hungary commits to improving its general governance issues in return for EU funds.

"Hungary has committed to several measures, including the limitation of financial activities to relevant market failures and implementation measures to prevent crowding out of private sector operators," the Commission said in a statement.

"This will ensure that MFB will not undercut private financial institutions active in the Hungarian market," it added.

The Council of the European Union approved Hungary's national recovery plan on Friday, marking another step in the process to give Budapest access to around €10 billion of EU funds that had been withheld on concerns over corruption.

($1 = 0.8750 euros)

(Reporting by Sudip Kar-Gupta; Editing by Kirsten Donovan)

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