New York (CNN Business) Five retailers have announced this week that they will start asking customers not to openly carry guns into their stores in states where open carry is legal. The moves represent a major shift in the way retailers are positioning themselves in the gun debate.

"We support the efforts of individuals and groups working to prevent gun violence, and continually review our policies and procedures to ensure our stores remain a safe environment," CVS said in a statement.

All of the retailers will still allow law enforcement officers to openly carry firearms.

Companies have faced increasing pressure from customers and employees to take action to prevent gun violence after a spate of mass shootings in recent weeks, including one inside a Walmart store in El Paso, Texas.

Walmart is the country's largest retailer. CVS and Walgreens are the largest and second-largest pharmacy chains. The companies have thousands of stores in places where customers may be opposed to restrictions on when and where they can carry guns, but all have now aligned themselves with the movement for gun reforms.

"Prohibiting open carry sends a very strong cultural signal that companies are siding with the safety of families," said Shannon Watts, founder of advocacy group Moms Demand Action, which has spent years pushing these and other companies to stop allowing open carry.

"They know their customers are with them on this ... they want to be on the right side of history but they also know that these actions are good for business," Watts said.

Advocates for gun control applauded the move to stop allowing open carry in retail locations after Walmart announced its new policy Wednesday. Walmart also announced that it would end some gun and ammunition sales, and would start pushing elected officials to adopt tighter gun laws.

Kris Brown, president of advocacy group Brady United, said the move by Walmart is "basically telling the NRA that logic does not support what they've been saying — this 'good guy with a gun' idea is patently false."

The NRA has repeatedly said that law abiding citizens with guns are the best protection from "bad guys with guns." It released a statement opposing Walmart's decision Wednesday.

Wegmans said in its statement Thursday that the policy is intended to keep customers and employees safer, and to help them feel more comfortable in its stores.

"The sight of someone with a gun can be alarming, and we don't want anyone to feel that way at Wegmans," the company said.

In a statement, the National Retail Federation noted Thursday that companies are constantly adapting their safety policies.

"Businesses in open carry states may choose to request that customers avoid openly carrying firearms, and that is a decision that NRF continues to leave up to individual retailers," the group's senior vice president of government relations David French said in a statement.

Enforcing the new policies

It is unclear exactly how the companies will enforce their requests that customers not openly carry in their stores. Laws in open-carry states generally allow private businesses to enact such policies, but differ in how they can or must be enforced.

In Texas, businesses wanting to prohibit customers from carrying handguns must put up large signs at the front of their stores in English and Spanish stating if open carry is not allowed, said Andrew Karwoski, deputy director of state policy for advocacy group Everytown for Gun Safety. The stores must have a separate sign if concealed carry is also prohibited.

In other open carry states, simpler signs — even a gun with a red circle and a slash through it — can suffice to communicate the policy, and violations may constitute a trespassing charge, Karworski said. Businesses can choose to ask customers to leave the premises if they violate the policy, or stores can contact law enforcement if the situation warrants it.

Walmart said it will take a "non confrontational" approach to enforcing the new policy by putting up signs outside stores announcing the request.

However, Karwoski said the method of enforcement is often less important than simply having the policy in place because "most gun owners are responsible," he said.

"They will respect stores' policies and just not carry there," Karwoski added.

Gun reform advocates now hope that Congress will notice the retailers' actions and pass legislation to stem gun violence.

"We plan to take this momentum to Washington next week when Congress gets back," Watts said.