FedEx promises to lap Amazon in 2021

It was the latest blow in a battle between the longtime shipping giant and the e-commerce behemoth

FedEx promised to lap Amazon in 2021 during its quarterly earnings call this week.

"The other thing is, is that I think if you think about all the positive things we've said and that we're seeing, as we get into 2021, we will start lapping Amazon," executive Alan Graf said. "We will have a lot more of the sixth and seventh day on our belt and we're going to be delivering millions of packages on Sunday for the rest of this fiscal year rolling into 2021."

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CEO Fred Smith echoed his optimism.

"FedEx is aggressively expanding North American package services for the rapidly growing ecommerce market to include year-round seven-day delivery. ... We had 37 million packages on Cyber Monday, and our plan was for 33 million," Smith said on the call.

FedEx deliverymen on LaSalle Street in Chicago.

Graf's statement comes amid news that Amazon has blocked third-party sellers, who make up more than half of all sales on its website, from using FedEx for Prime shipments due to declining performance. The ban comes ahead of some of the busiest shipping days of the year as Christmas is just over a week away.

“While this decision affects a very small number of shippers, it limits the options for those small businesses on some of the highest-demand shipping days in history and may compromise their ability to meet customer demands,” FedEx told FOX Business in a statement.

It was the latest blow in a battle between the longtime shipping giant and the e-commerce behemoth rapidly encroaching on its turf.

Amazon has been building out its fleet of cargo planes to chip away at a business long dominated by FedEx, UPS and the U.S. Postal Service. In June, it announced plans to lease an additional 15 aircraft to join the five it was already using. The company expects to have 70 planes in its fleet by 2021.

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FedEx, far from standing down, has taken aggressive action to get out ahead of Amazon.

In August, it severed ground-shipping ties with Amazon. A couple months before that, FedEx ended its relationship with Amazon’s air-freight division, stopping its delivery of about 200,000 Amazon packages each day.

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FOX Business' Jonathan Garber contributed to this report.