BUDAPEST—Hungary's central bank on Monday asked the International Monetary Fund, which helped rescue the country from the brink of insolvency in 2008, to close its Budapest office, as authorities here seek to reassert their sovereignty ahead of national elections next year.

In a letter to IMF Managing Director Christine Lagarde, the new central bank governor Gyorgy Matolcsy wrote that since the standby loan agreement between Hungary and the IMF is about to end, "we have come to the conclusion that it is not necessary...