BUDAPEST, June 29 (Reuters) - Hungary's central bank told local lenders on Saturday to immediately start reimbursing customers for erroneous charges made by Apple's electronic payment service earlier this week that has involved hundreds of thousands of accounts in Hungary.

Some 780,000 erroneous charges worth more than a combined 2 billion forints ($5.43 million) were made on Wednesday evening, the central bank said, adding the incident was due to a technical glitch at the international bank card partner of Apple's online store.

The statement from the National Bank of Hungary marks the first official indication of the scale of the issue. It did not name Apple's bank card partner.

The central bank, which is also in charge of financial sector regulation, said the issue was not the result of a cyber attack.

"The NBH is not satisfied with the pace of current procedures and calls on financial service providers to immediately start reimbursing clients," the bank said.

It added that the foot-dragging by Hungarian banks was "entirely unacceptable," also calling on lenders to start reimbursing clients who have not yet filed for compensation.

Apple could not be immediately reached for comment.

The central bank said it would launch an in-depth inquiry to see whether Hungarian banks' handling of complaints and reimbursements following the incident was in line with existing regulations. ($1 = 368.58 forints)

(Reporting by Gergely Szakacs; editing by Clelia Oziel)