Wal-Mart Stores, Inc. (NYSE:WMT) has taken another step forward in its quest to challenge Amazon.com (NASDAQ:AMZN) for e-commerce supremacy.

The world's largest retailer ditched its Amazon Prime-wannabe, Shipping Pass, which offered free three-day shipping for an annual fee of $49, and is instead offering free two-day shipping on all orders of $35 or more. 

It's a better deal for customers, as a majority of orders on the company's website are for more than $35, and Wal-Mart's success has historically come from offering rock-bottom prices without hurdles such as a membership fee, offering a different kind of value from Amazon Prime. Wal-Mart's own warehouse chain, Sam's Club, has always lagged behind Costco Wholesale.

An ad for Wal-Mart's  free two-day shipping program

Image source: Wal-Mart.

Wal-Mart is making more than 2 million items eligible for free two-day shipping, but that's much less than Amazon, which has over 50 million items available for free two-day shipping to Prime members. Wal-Mart's $35 minimum, however, is lower than Amazon's $50 minimum for non-Prime members, which does not promise two-day delivery -- though deliveries now often come in two days anyway, as the company's distribution network has vastly expanded in recent years.

Wal-Mart's U.S. e-commerce CEO, Marc Lore, who came to the company with the Jet.com acquisition last year, touted the move, saying in a press release: "I couldn't be more excited. We are moving at the speed of a start-up. Two-day free shipping is the first of many moves we will be making to enhance the customer experience and accelerate growth." With a nod to Amazon, Lore added, "In today's world of e-commerce, two-day free shipping is table stakes. It no longer makes sense to charge for it."

Will it be enough?

Wal-Mart's free two-day shipping offer is certainly a step in the right direction, as was its acquisition last summer of Jet.com, the company Lore founded. But there's also evidence that Amazon is stretching its lead over the retail giant.

Amazon's North American e-commerce sales jumped 22% in the fourth quarter, reaching $80 billion for the full year, and the company grabbed 53% of all e-commerce sales growth in the country last year, according to Slice Intelligence. That figure shows how dominant Amazon has become, taking more than half of new e-commerce sales in the country, which added $16 billion to its revenue last year. Retail giants like Wal-Mart and its competitors, as well as smaller e-commerce providers, are left to fight over the remaining growth.

Amazon continues to tighten the screws on its rivals, adding more members to Prime, and spreading Prime Now and Fresh to new cities.

According to Consumer Intelligence Research Partners, Amazon now has 65 million Prime members, or slightly more than half of total U.S. households. Wal-Mart's new two-day free shipping offer is unlikely to appeal to current Prime members, who have already coughed up the $99 annual fee to get free shipping and benefits including video streaming and access to the Kindle Lending Library.

But Wal-Mart can start by making a bid for non-Prime shoppers, who may currently be even more profitable to Amazon -- the company is running a wide shipping deficit, with net shipping costs totaling $7.2 billion last year. Shipping costs are growing faster than shipping revenue, evidence that membership fees from Prime are not keeping up with shipping costs.

Price vs. convenience

Wal-Mart can start by pressing its price advantage over Amazon. After all, the world's largest retailer reached the top of the food chain by promising everyday low prices that drove the mom-and-pop stores that couldn't compete out of business. Amazon stole some of that thunder as it also focused on rock-bottom prices during its early days, but the company has increasingly pivoted to competing on convenience over price, as its Prime membership program has come to dominate its domestic operations.

Amazon still retains a reputation as a low-cost provider, however, because it tends to discount the most popular items, but charge full price on less popular ones. In fact, the common perception that Amazon is less expensive than Wal-Mart is incorrect.

Wal-Mart needs to undo this perception through savvy marketing and aggressive pricing. Since it's significantly more profitable than Amazon, both in dollars and margin, it has the ability to slash prices even further to regain its reputation as the price leader. In fiscal 2016, Wal-Mart U.S.'s operating margin was 6.4%, compared to 3% last year for Amazon's North American e-commerce division.

From there, Wal-Mart needs to further leverage its Jet.com acquisition, making its "smart basket" technology -- an algorithm that lowers prices based on things the customer can control, like the number of items in their order -- available for all of its customers. I'd expect an announcement on that later this year, and many more such advances in the first full year of the Wal-Mart/Jet partnership. Lore has proven his e-commerce start-up mettle twice before, and hinted at further advances.

Still, Amazon continues to move at light-speed, opening up new fulfillment centers and unveiling innovations like the cashier-less Amazon Go store. Catching Amazon won't be easy, but Wal-Mart still has several advantages. With Lore's help, the company should be able to unlock them.

Jeremy Bowman has no position in any stocks mentioned. The Motley Fool owns shares of and recommends Amazon and Costco Wholesale. The Motley Fool has a disclosure policy.