Apple has agreed to refund at least $32.5 million to US customers for children's purchases from its online App Store without parental consent, US regulators said Wednesday.

The Federal Trade Commission said Apple also agreed to modify its practice -- which until now had allowed children to make purchases on an iPhone or iPad 15 minutes after a password was entered.

FTC chairwoman Edith Ramirez said Apple failed to inform parents of the 15-minute window that could allow children to make purchases ranging from one dollar to $100 for each app.

Ramirez told reporters that because of the loophole, "children ran up millions of dollars in charges without their parents' knowledge and consent," a violation of federal rules.

Consumers "will be obtaining full redress" for any unauthorized charges, she added.

Ramirez said the FTC believes there are "many thousands of consumers which were impacted" and could get refunds.

She said the consent decree signed with Apple sets a minimum of $32.5 million, with no maximum. But if the refunded amount is less than $32.5 million, the balance will be paid to the regulatory agency.

Apple chief executive Tim Cook, in a letter to employees obtained and posted by the website 9to5mac, said the company has already been following the practices requested by the US regulators.

"The consent decree the FTC proposed does not require us to do anything we weren't already going to do, so we decided to accept it rather than take on a long and distracting legal fight," Cook was quoted as saying.

Cook's memo said Apple had "heard from some customers with children that it was too easy to make in-app purchases, so we moved quickly to make improvements."

He said the company sent emails to 28 million App Store customers offering refunds and that "when some emails bounced, we mailed the parents postcards."

"In all, we received 37,000 claims and we will be reimbursing each one as promised," Cook said in the memo.

Ramirez told reporters however that the FTC settlement "provides more robust relief" than Apple's voluntary actions.

She said under the agreement, Apple must notify parents of the 15-minute window that allows further app purchases after a password is entered.

Ramirez would not comment on any other investigations but said the agency "is obviously concerned" about other companies in the mobile space where children may be able to make purchases without parental consent.