NEW YORK — Walmart says it will discontinue the sale of handgun and short-barrel rifle ammunition and also publicly request that customers refrain from openly carrying firearms in stores even where state laws allow it.

The announcement comes just days after a mass shooting claimed seven lives in Odessa, Texas, and follows two other back-to-back shootings last month, one of them at a Walmart store.

The Bentonville, Ark.-based discounter said Tuesday it will stop selling handgun ammunition as well as short-barrel rifle ammunition, such as the .223 caliber and 5.56 caliber used in military style weapons, after it runs out of its current inventory.

It will also discontinue handgun sales in Alaska. Walmart stopped selling handguns in the mid-1990s, with the exception of Alaska.

The latest move marks its complete exit from that business and allows it to focus on hunting rifles and related ammunition only.

“We have a long heritage as a company of serving responsible hunters and sportsmen and women, and we’re going to continue doing so,” according to a memo by Walmart’s CEO Doug McMillon to be circulated to employees Tuesday afternoon.

The retailer is further requesting that customers refrain from openly carrying firearms at its Walmart and Sam’s Club stores unless they are law enforcement officers. However, it said that it won’t be changing its policy for customers who have permits for concealed carry. Walmart says it will be adding signage in stores to inform customers of those changes.

Last month, a gunman entered a Walmart store in El Paso, Texas, killing 22 people with an AK-style firearm that Walmart already bans the sale of and marking the deadliest shooting in the company’s history. Texas became an open carry state in 2016, allowing people to openly carry firearms in public.

Walmart’s moves will reduce its market share of ammunition from around 20% to a range of about 6% to 9%, according to Tuesday’s memo. About half of its more than 4,750 U.S. stores sell firearms.

The nation’s largest retailer has been facing increasing pressure to change its gun policies by gun control activists, employees and politicians after the El Paso shooting and a second unrelated shooting in Dayton, Ohio, that killed nine people. A few days before that, two Walmart workers were killed by another worker at a store in Southaven, Miss.

In the aftermath of the El Paso shooting, Walmart ordered workers to remove video game signs and displays that depict violence from stores nationwide. But that fell well short of demands for the retailer to stop selling firearms entirely.