"The expected change regarding the use of Visa credit cards on Amazon.co.uk will no longer take place on January 19," the company said in an email to customers.
"We are working closely with Visa on a potential solution that will allow customers to continue using their Visa credit cards on Amazon.co.uk."
It said customers could still use Visa debit cards along with Mastercard and Amex credit cards and Eurocard.
A Visa spokesman said Monday: "Amazon customers can continue to use Visa cards on Amazon.co.uk after January 19, while we work closely together to reach an agreement."
Visa had said in November that it was "very disappointed that Amazon threatened to restrict consumer choice".
An EU enforcement ceiling for fees charged by card issuers is no longer in place in the UK after Brexit.