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The former Beatle made the gesture in front of more than 60,000 fans that had gathered to watch him perform at the capital's FedEx Field on Saturday night, reports NBC Washington.
"This is one that we think Barack might want to sing to someone in his house," he quipped, before launching into the love song.
However, Michelle was not in attendance to hear the dedication having already left with her husband and children for a vacation at Camp David.
This is not the first time that McCartney has voiced his admiration for the president's wife. Last year, he told Sky News that he wanted "the opportunity to sing" to the style icon, adding: "I have a little song ready."
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