The U.S. learned about the possible location of an American hostage now being threatened with death by militants in Yemen a week before the Pentagon launched a mission aimed at rescuing him last month, U.S. officials said.

But some U.S. officials said they now believe delays in the planning and approval of the operation contributed to its failure to free journalist Luke Somers. Others said there was incomplete intelligence and that the Pentagon and White House moved quickly to approve the operation once it was presented.

The planning of the raid has come under scrutiny as the al Qaeda affiliate in Yemen late Wednesday released a video showing Mr. Somers, 33 years old, and threatening to kill him by the end of the week.

In a video obtained by the SITE Intelligence Group, which tracks jihadist activities, Mr. Somers was shown saying he was “certain that my life is in danger.”

Militants moved at least two of the hostages they had been holding in a cave hours before Joint Special Operations Command presented their rescue plan to the Pentagon for approval. Intelligence officials, however, believed Mr. Somers, at that point, hadn’t been moved and remained in the cave, U.S. officials said.

A team of American and Yemeni commandos conducted the rescue raid on a hillside cave in Yemen early on Nov. 25. The commandos ultimately freed eight people, mostly Yemenis, but Mr. Somers wasn’t there. Some officials said they now wonder if he was ever in the cave.

This wasn’t the first such rescue attempt foiled when hostages were moved at the 11th hour. U.S. officials are now debating why a second hostage rescue in the past six months ended in failure.

Some officials earlier said the failed commando mission to rescue James Foley, a journalist beheaded by Islamic State in Syria in August, was also characterized by imperfect intelligence and a long planning and approval process.

November’s attempted rescue was similarly the result of inadequate intelligence and a cautious approval process within the Obama administration, some officials said, which may have contributed to the failure.

Adm. John Kirby, the Pentagon press secretary, disputed that characterization. He said the decision-making process was expeditious.

“This went from theory to execution at a fast clip,” he said. “Every leader in the chain of command recognized both the peril and the promise this operation held.”

JSOC developed intelligence around Nov. 17 that Mr. Somers was possibly being held in a cave on a hillside in a remote part of Yemen.

The intelligence was initially viewed as shaky, officials said, but as planning went on, military intelligence officials began to have a higher degree of confidence.

Early on Nov. 21, the U.S. learned that at least two of the hostages had been moved from the cave. It wasn’t clear if Mr. Somers was one of the people moved, although intelligence agencies believed he was still being held there.

Later, JSOC formally presented a plan to rescue Mr. Somers to the Pentagon midmorning on Nov. 21.

Military planners told the Pentagon they would execute the mission in a nighttime raid the following day after the plan was approved.

Inside the Pentagon, Adm. James Winnefeld, the vice chairman of the Joint Chiefs of Staff, conducted a quick review of the mission. He approved it and it was sent to Defense Secretary Chuck Hagel at 4 p.m.

Mr. Hagel immediately approved it and sent it to the White House, a senior defense official said.

At the White House, counterterrorism chief Lisa Monaco held a classified video teleconference on the afternoon of Nov. 22 to discuss the raid.

At the end of the meeting, Ms. Monaco said the White House would make a decision after senior members of the National Security Council had a chance to weigh in by the morning of Nov. 23.

After written approvals were submitted, Mr. Obama, who was traveling back to Washington from Las Vegas, approved the raid, officials said.

Some officials said they believe the raid should have been planned and approved more quickly. Others said they believe military planners should have informed the Pentagon of the potential for a rescue operation sooner.

“Should it take this long to get approval when you have an operation ready to go,” asked a U.S. official. “We should have approved this in a matter of hours rather than days.”

But other officials said the speed of approvals had no impact on the mission.

The intelligence was imperfect, they said. Some officials said they believe Mr. Somers may never have been in the cave while others said they believe he could have been moved undetected.

“The intelligence may have been faulty,” said a senior administration official. “There was broad consensus he was there when the raid was authorized.…Some people now suspect that he was never there in the first place.”

A senior defense official said the approval at the Pentagon and the White House went quickly, considering the difficult circumstances of the hostage situation.

The operation, the official said, “wasn’t a no-brainer.” The official said the presence of hostile forces, hostages from multiple countries and the political turmoil in Yemen all presented challenges.

Bernadette Meehan, the spokeswoman for the National Security Council, also defended the White House’s response time.

As soon as the U.S. government had reliable intelligence and an operational plan, the president authorized the Department of Defense to conduct an operation to recover Mr. Somers,” she said. “The president authorized this action following the unanimous recommendation of his national-security team.”

By Julian E. Barnes,

Adam Entous and

Carol E. Lee - WSJ