The e-commerce giant launched its express, same-day delivery service, Prime Now, on Thursday morning in Singapore, but by that afternoon the service seemed to have become unusable.
Many users in Singapore were unable to select a delivery window for their purchases to be delivered at the checkout screen. A message stated that all remaining delivery windows "for today and tomorrow are currently unavailable," and that users should check in later for updates.
On Friday, the messaging on the checkout screen was updated to say that Amazon was "working hard to open up more capacity as soon as possible."
Some items listed also appeared to be either in low supply or to have run out of stock on Friday morning.
When contacted by CNBC, Amazon said that users were unable to check out because they were "sold out" of delivery availability.
The company said in an official statement that "Singapore loves Prime Now, and we are delivering thousands and thousands of orders each day." Most reports on local media indicated delivery could be selected for only a few hours after the initial launch.
In its statement to CNBC, Amazon added: "Due to great customer response, delivery windows are currently sold out. We are rapidly opening up new windows to ensure we can continue delighting customers in Singapore."
The Prime Now service is available in Singapore through the app, which can be downloaded on Google's Play store and Apple's App store. Prime Now is part of Amazon's Prime membership service and was launched in December 2014 in New York. To-date, the service is available in more than 50 cities in nine countries, including Berlin, London, Madrid, Rome and Tokyo.
There are several delivery options given: For orders below 40 Singapore dollars ($29.48), users pay a S$5.99 delivery fee; orders above S$40 are delivered free in a two-hour delivery window. For those wanting to get their goods within an hour, they pony up S$9.99 per order.
— CNBC's Leslie Shaffer contributed to this report.