WASHINGTON – After refusing for more than two years to indulge the most corrosive of conspiracy theories questioning his legitimacy, President Obama finally decided that he’d had enough.

He was frustrated and annoyed that questions about where he was born — once the province of the political fringe and more recently fanned by showman and real estate mogul Donald Trump — had arisen even in an interview last week with ABC News anchor George Stephanopoulos.

The “birther” question had become a distraction, one that was getting in Obama’s way as he tried to sell the country on his approach to long-term deficit reduction.

On April 19, Obama ordered White House counsel Robert Bauer to find out what it would take to retrieve a longer and more detailed version of his Hawaiian birth certificate, a document not routinely released by state authorities.

That set into motion several days of intense, secret maneuvering that culminated in an extraordinary moment Wednesday. The president appeared in the White House briefing room with evidence that he had indeed been born in the United States, as the Constitution requires.

In a six-minute statement, Obama alternately poked fun at the “sideshows and carnival barkers” that had made such a declaration necessary and pleaded for the media and political world to focus on the serious challenges that face the nation.

“We do not have time for this silliness,” Obama said. “We’ve got better stuff to do. I’ve got better stuff to do. We’ve got big problems to solve.”

Some of the president’s conservative critics have pushed the theory that Obama, whose father was Kenyan, was born in Africa, as a way to question his constitutional legitimacy and even his basic American-ness.

It is a falsehood that has gained remarkable currency. The most recent CBS/New York Times poll suggests about one-quarter of Americans believe it to be true. Among Republicans, 45 percent said they think Obama was not born in the United States.

The overall number has risen by 5 percentage points over the past year, driven largely by a 13-point uptick among Republicans. Among independents, the number has remained steady, around one-quarter.

Even before the White House procured a copy of the complete document and posted it on the Internet, there had been ample evidence to show that Obama had indeed been born in Hawaii nearly two years after it became a state. During the 2008 campaign, he had produced the standard version of his birth record, and newspaper birth announcements at the time corroborated it. Some 70 lawsuits challenging Obama’s birthplace had been dismissed by various courts.

Innuendo, of course, has always hung around backstage in politics — and the general rule has always been that the best way to handle it is to ignore it.

But today’s is a brutal, instantaneous media culture. Obama — the nation’s first black president, and one who was raised in multicultural surroundings — has been the target of more than his share of toxic, sometimes incongruous rumors.

During the 2008 campaign, he simultaneously battled criticism over his membership in a Christian church with a controversial pastor and murky tales that he was secretly a Muslim. At first, his attitude as a candidate was to stay above the fray; he decided to reverse course when his wife, Michelle, was falsely accused of using a racial epithet against whites. At that point, Obama ordered the launch of a website titled “Fight the Smears.”

A similar instinct drove his decision last week to confront the speculation, aides said.

“The president believed the distraction over his birth certificate wasn’t good for the country,” White House communications director Dan Pfeiffer wrote in a blog post on the White House website. “It may have been good politics and good TV, but it was bad for the American people and distracting from the many challenges we face as a country.”

Obama told donors in New York on Wednesday night: “Part of what happened this morning was me trying to remind the press and trying to remind both parties that what we do in politics is not a reality show. It’s serious.”

On April 22, Obama signed a letter to Hawaii officials requesting the document, which they replied could be made available Monday. Obama dispatched his outside counsel, Judy Corley, to Hawaii to retrieve it, and she delivered it to the White House on Tuesday night.

The timing for Obama’s appearance was in some ways surprising. It came on a day when the top story might otherwise have been news of changes in the administration’s national security team. White House officials said they wanted to release the paperwork as quickly as possible after receiving it, to pre-empt any further conspiracies about whether it had been doctored. They also were aiming for an element of surprise, catching off-guard a White House press corps that had no hint the administration might make this move.