Amazon.com Inc., the largest online retailer, offered customers $20 gift cards and refunds on shipping charges after an avalanche of orders caused United Parcel Service Inc. to miss delivery of some packages by Christmas.

Amazon cited failures in UPS’s transportation network in messages to customers, saying its own fulfillment centers processed customers’ orders in time for holiday delivery. Amazon is reviewing the performance of the delivery carriers, spokeswoman Mary Osako said in an e-mail.