Analysts on average had expected a 3.1 percent drop in global same-restaurant sales, according to research firm Consensus Metrix.
In the United States, same-restaurant sales fell 2.8 percent. Monthly same-store sales have been down or flat in the region since November 2013.
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Thompson has presided over a period of disappointing results from the United States, due in part to internal missteps, competition from burger chains including Burger King Worldwide and Wendy's and cautious spending by the lower-income consumers that frequent the chain.
McDonald's is replacing its U.S. president for the second time in two years.
Same-restaurant sales in Europe, the company's biggest region by sales, fell 0.7 percent.
In Asia/Pacific, Middle East and Africa, sales fell 14.5 percent, hurt mainly by a food scandal in China that drove away diners and forced the chain to scramble to find new suppliers of ingredients for its Chicken McNuggets and Big Macs.
The company said it expects the food scare to hurt third-quarter profit by 15 cents to 20 cents per share.