TORONTO — Royal Bank says it will recover by Thursday from a computer glitch that kept millions of transactions out of Canadians' bank accounts for two days this week.

The big bank said its account balances for transactions made Tuesday and Wednesday should be updated in its customer accounts by Thursday morning.

"We recognize this has caused not only our own clients but also clients of some other institutions considerable inconvenience and for this we sincerely apologize," Rod Pennycook, an executive vice-president at the bank, said in a statement late Wednesday.

"We want to assure all those affected that their money is safe and secure. We are now completing the process of rechecking and verifying transactions that took place between May 31 and June 2."

The bank said the processing disruption, which occurred during a routine programming update to one of the Royal's computer systems, resulted in some deposits, withdrawals and payments made on May 31 and June 1 not being reflected in customer account balances.

Canada's largest bank (TSX:RY), which has more than 12 million personal, business and public sector customers, said it will cover all service fees and overdraft charges connected with the problem.

In trading on the Toronto Stock Exchange on Wednesday, Royal shares rose eight cents to close at $59.28.