"We do not have any suspects at this time and no security video footage."
Locals have been asked to watch for anyone acting suspiciously or using large amounts of money.
Police are also calling for a person who was seen looking into the bank late on the Tuesday night to come forward.
There are three banks on Aitutaki and the theft is the biggest bank-related crime to be perpetrated on the island.
Bank of the Cook Islands managing director Vaine Nooana-Arioka said the branch was closed for one day last week, as police carried out their investigations at the scene.
She said reports that the money was secured by a single padlock were not true.
Mrs Nooana-Arioka said staff were positive that the culprit or culprits would be found and the money returned.
"With ongoing police investigations, [the bank] will not make further media statements except to encourage the community on Aitutaki and elsewhere to contact the Cook Island police with any information that will help lead to a successful prosecution."