Hester said a failed software upgrade had caused the problems, which began Tuesday and have delayed posting of credits and debits to millions of customer accounts.
Hester told Sky News on Monday that the problem had been fixed and the backlog was clearing.
Customers of RBS and two banks it owns — NatWest and Ulster Bank — have been affected by the glitches.
Customers have complained of bills and salaries going unpaid and delays in closing home purchases because money was not being credited to accounts.
Some 1,200 bank branches opened Sunday for the first time to help clear the backlog.