For the Postal Service, which lost nearly $16 billion last year, first-class mail delivery, particularly on Saturdays, is often a money loser, whereas package delivery is profitable.

The deal, announced on Sunday and taking effect immediately, in time for the holiday shopping season, gives the Postal Service a chance to take some business from United Parcel Service and FedEx, which do not deliver on Sundays. Now, some orders that would have been handled by either of those carriers for Monday delivery will go through the Postal Service and arrive on Sunday.

The Postal Service said it expected to make more such deals with other merchants, seeking a larger role in the $186 billion e-commerce market. Amazon.com would not say if it would try to arrange Sunday deliveries with other parcel carriers.