Kroger, the largest U.S. supermarket operator, is the latest high-profile company caught in the battle over gun rights and gun control in the United States.
Moms Demand Action for Gun Sense in America (MDA), backed by former New York City Mayor Michael Bloomberg, is petitioning Kroger to prohibit guns in its more than 2,600 U.S. stores, which include Food 4 Less, Harris Teeter and Smith's.
Kroger said it does not want to put its employees in a position of having to confront a customer who is legally carrying a gun, so its long-standing policy has been to follow state and local laws.
"We know that our customers are passionate on both sides of this issue and we trust them to be responsible in our stores," the company said without elaborating.
"We spend a lot of time with our kids at the grocery store. How can we possibly know if an armed person at a Kroger store is a responsible gun owner, or a serious threat to our children?" said Shannon Watts, a former public relations executive who founded MDA.
Watts said her group made its decision after gun rights supporters demonstrated at some of the company's stores. It also discovered that there had been shootings on Kroger properties over the years.
Starbucks Corp had a gun policy similar to Kroger's up until 2013, when it became the target of both sides in the gun debate. The coffee chain changed its policy by asking customers to leave their guns at home.
"We are forcing American businesses to take a stand," Watts said.
Bloomberg, a billionaire and staunch gun control advocate, became more outspoken on the issue after a gunman killed 20 children and six adults at a Newtown, Connecticut, elementary school in 2012. In April, he committed to spend $50 million on a grassroots network called Everytown for Gun Safety. MDA is under the Everytown umbrella.
The National Rifle Association, the largest U.S. lobby group for gun rights, did not immediately respond to a request for comment.
More than 40 states have so-called "open carry" laws. Proponents have taken guns, including assault weapons, to restaurants and stores to draw attention to their cause.
John Pierce, co-founder of OpenCarry.org, said MDA is "trying to put businesses in a position they don't want to be in."
He predicted that Kroger would be less likely than Starbucks or Target to move its position since its customers hail from a broader political spectrum.
Pierce said carrying a gun into a store is no more political than a same-sex couple going to a store to shop.
"They are simply going to the grocery store," he said.