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LONDON — President Obama, who had urged British voters not to turn their backs on the European Union, said Friday that the U.S. would “respect their decision” to do so and that the “special relationship” across the Atlantic would continue.

Obama said that, despite their upcoming divorce, the U.S. would continue to regard both Britain and the E.U. as “indispensable partners of the United States.”

Britain’s membership in the North Atlantic Treaty Organization remained “a vital cornerstone of U.S. foreign, security, and economic policy,” Obama said. He also commended the E.U. for promoting stability, prosperity and democratic values.

Still, Britain’s vote to leave the E.U. is a major disappointment to the White House. The U.S. has long regarded Britain, its closest ally, as a bridge to the rest of Europe and sees its usefulness as diminished if it is no longer a member of the E.U.

On a visit to London in April, Obama encouraged Britons to vote to remain in the trading bloc and warned that, if they left, their country would be sent to the “back of the queue” in terms of striking a new trade deal with the U.S. He said his first priority was to seal a trade pact with the E.U.

Although Obama is generally popular here, many Brits bristled at what they perceived as a foreign leader telling them what to do.