The Amazon pledge came after UPS in particular came under fire for late packages despite vows from retailers to meet a December 25 deadline.
Some customers took to Twitter to voice their displeasure, likening one or both delivery giants to the "Grinch who stole Christmas."
Amazon pointed the finger squarely at the delivery companies. The online retail giant did not give estimates for the number of affected shoppers.
"Amazon fulfillment centers processed and tendered customer orders to delivery carriers on time for holiday delivery," said Amazon spokeswoman Mary Osako. "We are reviewing the performance of the delivery carriers."
Walmart also will provide gift cards to customers who did not receive packages by the promised deadline, the New York Times reported.
Walmart did not immediately respond to a request for comment.
"UPS experienced heavy holiday volume and is making every effort to get packages to their destination as quickly as possible," UPS said on its website. "UPS has resumed normally scheduled service on December 26."
A FedEx spokesperson also reported a "surge" in volume, but said the rise was typical.
"We had minimal service disruptions despite the increase in volumes, and are working directly with customers who may have experienced any delays," said the FedEx spokesperson.
The delivery woes suggested the retail sector is still adjusting to shifting customer behavior with the rise of online shopping.
Analysts had expected brick and mortar shopping to rise just 3-4 percent in 2013, but online shopping to jump 13-14 percent.
More retailers have promised to execute Christmas-deadline deliveries ordered later and later in the season.
Amazon characterized its overall holiday shopping season as the "best ever" in the company's history.
Particularly popular was the "Amazon Prime" service, which provides free two-day shipping services and streaming of some television shows and movies for $79 a year.
Amazon said it signed up more than one million customers for its "Prime" service in the third week of December.