In full-page ads running Wednesday in The New York Times and the Chicago Tribune – the hometown paper of the Illinois-based McDonald’s – the fast-food chain is proposing the “McWhopper,” a hybrid of each company’s signature Big Mac and Whopper burgers that will be sold for one day in one pop-up store in one city.

That city, Burger King is proposing, would be Atlanta, a meeting point between both company’s headquarters. The marketing stunt would be held on Sept. 21, with proceeds benefiting the anti-conflict nonprofit Peace One Day.

Burger King has also set up a website listing out its proposal, even suggesting a recipe for the new hybrid burger: it will contain six ingredients from the Big Mac (like cheese and special sauce) and six from the Whopper (like the flame-grilled patty and onions).

McDonald’s responded on Facebook Wednesday morning:

Dear Burger King,

Inspiration for a good cause… great idea.

We love the intention but think our two brands could do something bigger to make a difference.

We commit to raise awareness worldwide, perhaps you’ll join us in a meaningful global effort?

And every day, let’s acknowledge that between us there is simply a friendly business competition and certainly not the unequaled circumstances of the real pain and suffering of war.

We’ll be in touch.

-Steve, McDonald’s CEO

P.S. A simple phone call will do next time.

Such publicity could help provide needed positive news for both companies, each struggling to improve revenues in a new health-conscious, “fast-casual” dining environment. Burger King, owned by private equity group 3G Capital, temporarily lost its ranking as the world’s No. 2 burger chain to Wendy’s last year. Meanwhile, McDonald’s recently reported a 10% drop in quarterly sales, with new CEO Steve Easterbrook calling the results “disappointing”.