Donald J. Trump publicly retreated from his “birther” campaign on Friday, tersely acknowledging that President Obama was born in the United States — and effectively conceding that the conspiracy theory he had promoted for years was baseless.

Mr. Trump made no apology for and took no questions about what had amounted to a five-year-long smear of the nation’s first black president. Instead, he claimed, falsely, that questions about Mr. Obama’s citizenship were initially stirred by the Democratic presidential nominee, Hillary Clinton, in her unsuccessful primary contest against Mr. Obama in 2008.

Still, Mr. Trump’s brief remarks, tacked on to the end of a campaign appearance with military veterans at his new hotel in downtown Washington, represented a sharp reversal from a position he had publicly maintained, over howls of outrage from all but the far-right extreme of the political spectrum, since 2011.

“President Barack Obama was born in the United States, period,” Mr. Trump said. “Now, we all want to get back to making America strong and great again.”