NEW YORK (TheStreet) -- "We want to be a modern, progressive burger company," said McDonald's (MCD) - Get McDonald's Corporation (MCD) Report CEO Steve Easterbrook last month on an analyst call.

Well, McDonald's head cheese may have missed a golden opportunity to deliver on that mission, and in the process help turn around its stagnant sales trend. In an open letter to its rival published in full-page ads in the New York Times and Chicago Tribune on Wednesday, Restaurant Brands' (QSR) - Get Restaurant Brands International Inc Report Burger King chain proposed that the two burger titans set aside their differences to create the "McWhopper."

The item would combine the best ingredients from each chain's signature hamburgers and be offered at one pop-up location in Atlanta on National Peace Day, September 21, with the proceeds benefiting Peace One Day. Burger King did not list the ingredients it planned to use for the McWhopper, but did go as far as to create an image of what the creation and its packaging might look like. 

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Burger King's latest marketing stunt prompted a rather unfriendlyresponse from Easterbrook on McDonald's Facebook page. "We love the intention, but think our two brands could do something bigger to make a difference," said Easterbrook, adding "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." 

Easterbrook closed his message with a bit of stern fatherly-type advice for its rival: "A simple phone call will do next time."

Responses to Easterbrook's letter on Facebook drew the usual fire from people who generally dislike McDonald's. But more significantly, in rebuffing Burger King's playfulness, McDonald's has neglected a chance to drum up some positive buzz on social media and begin to alter its tarnished reputation among consumers.

Mashing together two of the most iconic fast foods of all-time for a single day would likely be a big-time social media spectacle that could lure in curious customers for both chains across the country. Furthermore, fast-food mash-ups have been all the rage this year, receiving generally warm receptions by consumers. 

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Clever, bold marketing like this has worked wonders for hard-charging Burger King, which has come at the expense of McDonald's sales.

Burger King's adjusted second quarter earnings per share came in at 30 cents compared to the 25 cents analysts were estimating. Same-restaurant sales at Burger King U.S. surged 7.9% in the second quarter, quicker than the 6.9% gain grilled up in the first quarter.

Burger King's CEO Daniel Schwartz attributed part of the strength in the quarter to the return of Burger King's notorious King mascot, who made high-profile TV appearances at the Kentucky Derby in June and the Mayweather-Pacquaio fight in May to much social media fanfare. 

More recently, Burger King aggressively took to social media to generate interest in new spicy chicken fries. Name of the marketing campaign: "Offensively Spicy." 

"We wanted to create something as spicy as sh**, that it was so spicy that it may even offend you," said Eric Hirschhorn, Burger King's chief marketing officer for North America to TheStreet.

Meantime, the Golden Arches is mired in a serious sales slump due to the poor perception of its food quality and fewer exciting new products compared to Burger King and other competitors. Despite new menu items such as the Sirloin Third Pound Burger and various regional items such as the McLobster in Boston, McDonald's reported a 2% same-store sales decline in the U.S. for the second quarter, the seventh consecutive quarter of declining U.S. same-store sales.

Burger King offered a calculated olive branch to its rival, but McDonald's chose to break it in half. McDonald's may end up being the one suffering for it.