WASHINGTON — For President Barack Obama, the test now is in the telling.

The White House has struggled to craft its account of the audacious raid that killed Osama bin Laden for both a jubilant American public and a skeptical Muslim world, correcting parts of its narrative, withholding others and, after internal debate, deciding not to release photos that could be considered too provocative.

“We review this information and make these decisions with the same calculation as we do with so many things — what we’re trying to accomplish and does it serve or in any way harm our interests, not just domestically but globally,” White House spokesman Jay Carney said.

The White House deliberations and disclosures illustrated the public relations challenge for the president, eager on the one hand to quickly capitalize on a remarkable military achievement while at the same time seeking a tone that did not gloat or incite the Muslim world. In that environment, Obama tried to portray an air of business as usual even as his administration exulted in the aftermath of the feat carried out by Navy SEALs.

No doubt, the White House sought to carefully manage the story with presidential stagecraft. Obama emerged to make a dramatic statement announcing bin Laden’s death Sunday night. On Monday, the White House released a photograph portraying the president and his national security team watching intently at an unseen screen as the raid unfolded 7,000 miles away. And on Thursday, Obama plans to go to the World Trade Center site in New York City to remember victims of the 9/11 terrorist attack by bin Laden’s al-Qaida operatives.

Obama clearly was benefiting from the attention. His job approval rating spiked to 57 percent in a New York Times-CBS News poll and 56 percent in a Washington Post-Pew Research Center poll. It recently had been below 50 percent.

Yet, the White House found it had to backtrack and revise its own account of what happened in the raid. Administration officials said bin Laden was not armed after having said on Monday that he resisted and was killed in a firefight. They also backed away from earlier statements that bin Laden or his defenders used a woman as a human shield.

President Barack Obama told CBS in an interview to be aired Sunday that he decided not to release photographs of bin Laden’s corpse, an image Carney described as “gruesome.” The decision had clearly been the subject of debate; CIA Director Leon Panetta had predicted Tuesday in an NBC interview that “ultimately a photograph would be presented to the public.”

Central to the discussion were unfounded claims that bin Laden was still alive and administration officials were eager to tamp down any conspiracy theories.

But releasing the photo had significant drawbacks and several lawmakers counseled against making the images public.

“A graphic image such as that has the potential to inflame a community just out of its sheer shock value,” said John Ullyot, a former Republican Senate Armed Services Committee aide and Marine intelligence officer. “Even the release of a graphic photo might not close the book in some people’s minds.”

Ari Fleischer, press secretary to President George W. Bush, cautioned against releasing explosive photographs. “This story already has an exclamation point on it,” he said.

In addition to killing bin Laden, the Navy SEALs killed three other men in bin Laden’s compound. One woman was killed in what officials described as crossfire.

Obama was publicly silent about the raid Tuesday, even in the presence of reporters and photographers at the start of an early afternoon Cabinet meeting. But top aides were on television providing accounts of the assault and most of the daily news briefing was dominated by the raid.

Even as they offered new details or corrected old ones, the White House kept others to themselves. Officials were reluctant, for example, to publicly discuss what Obama and his team were watching so intently in the photo they had promoted the day before.

Fleischer said Obama also faces a challenge as he moves toward his re-election campaign.

“That’s where these issues will start to ricochet,” Fleischer said, recalling the criticism lobbed at Bush when he mentioned the 9/11 attacks during his 2004 campaign. “A lot of it is unwarranted; presidents should talk about accomplishments.”

The success of the raid also raised difficult questions for the administration about whether the use of waterboarding or other harsh interrogation techniques under the Bush administration had elicited some of the intelligence that led to bin Laden’s lair. Obama has been a staunch critic of those methods.

“It simply strains credulity to suggest that a piece of information that may or may not have been gathered eight years ago somehow directly led to a successful mission on Sunday,” Carney said. “That’s just not the case.”

In his interview with NBC, Panetta was not as adamant. “They used these enhanced interrogation techniques against some of these detainees,” he said. “But I’m also saying that, you know, the debate about whether we would have gotten the same information through other approaches I think is always going to be an open question.”

As discussions and raid details swirled throughout the administration, Obama himself sought to convey a return to normal Tuesday. He held a Rose Garden event to salute exceptional teachers and met with Hispanic members of Congress to discuss changes in immigration law.

While Obama travels to New York on Thursday, Vice President Joe Biden plans to convene a meeting with congressional negotiators to discuss long-term spending proposals. And on Friday, Obama once again will confront the economic realities that have dogged his presidency when the Bureau of Labor Statistics releases April unemployment figures.

“This train never stops,” Carney said.