The latest fight between FedEx and UPS isn't about shipping. It's about ties to the National Rifle Association.

UPS (UPS) said in a statement Wednesday that it is not a sponsor of the NRA and that it does not offer a special discount for NRA members.

That comes after its competitor, FedEx (FDX) — itself fielding criticism from activists for standing by its NRA shipping discount — accused UPS of having a relationship with America's top gun lobby.

"For shipping from its online store, the NRA uses UPS and not FedEx," FedEx said on Tuesday.

UPS maintains that it's a "common carrier," and that if a shipper like the NRA "is engaged in lawful conduct, has an item that is legal to ship, and agrees to the company's terms and conditions regarding the shipment, UPS will transport their shipment from origin to destination."

Both UPS and the U.S. Postal Service are listed as shippers for the NRA online store, which "includes accessories such as ball caps, T-shirts, holsters and hunting and sporting goods merchandise," UPS added.

On Wednesday, FedEx said that UPS provides "discounted shipping rates to the NRA, which uses UPS for shipping."

UPS said in response that it does not disclose the terms of its customer contracts. "UPS provides highly competitive commercial terms," the company said in a statement.

The NRA has become a controversial partner for many companies in the wake of the high school shooting in Parkland, Florida earlier this month, which left 17 people dead.

A number of companies that offered discounts to NRA members, such as Hertz (HTZ), Delta (DAL) and MetLife (MET), said in the past week that they would end their programs.

Related: Companies learn the hard way: There's no easy way to take sides in polarized America

Still, many have found it difficult to wade into the public battle over gun rights without taking political heat or alienating part of their customer base.

Delta, for example, is now in a showdown with Georgia Republicans, who are threatening to block a state tax break that would benefit the airline.

FedEx made news on Monday when it said it would keep its discount for NRA members.

The company said in a statement that it "has never set or changed rates for any of our millions of customers around the world in response to their politics, beliefs or positions on issues," and that the NRA is one of "hundreds of organizations" that pay discounted rates for shipping.

In the same statement, FedEx tried to distance itself from the NRA on gun policy, saying that the company believes that assault rifles should only be available for military use.

Despite the attempted balancing act, FedEx continued to receive negative social media attention, and had to release a follow-up statement on Tuesday. That's when FedEx sought to divert attention to UPS.

"FedEx is aware there are some continuing concerns related to the NRA, and we want to provide important, clarifying facts," the company said. " ... FedEx has never provided any donation or sponsorship to the NRA."