Gen. David Petraeus, the top U.S. commander in Afghanistan, will launch an investigation into the failed attempt to rescue Linda Norgrove, 36, Cameron said.

NATO and British officials had said earlier she was killed by her captors, who detonated an explosive.

But Cameron said Monday that statements made about Norgrove's death over the weekend were "highly likely to have been incorrect," although they were made "in good faith."

Petraeus contacted him Monday morning, he said, with new information.

But Cameron said he could not make a firm statement about the cause of her death until the investigation is complete. It will be a joint investigation between the United States and United Kingdom, he said.

U.S. President Barack Obama called Cameron on Monday to offer condolences for Norgrove's death, according to a statement from the Downing Street press office.

"The Prime Minister and the President agreed that it was now essential to get to the bottom of what had happened in the course of the rescue operation. They looked forward to close co-operation between the UK and US authorities on the investigation and agreed to stay in close touch as it moved forward," it read.

The investigation will start in the next day or two and will be led by a senior officer from U.S. Central Command, an International Security Assistance Force official told CNN.

One of the key components in determining what went wrong will be the autopsy, which will be carried out by British officials, the ISAF officer said.

Cameron and Petraeus are to meet Thursday in London. "It's a long-standing meeting and has been in the diary for a number of weeks," the Downing Street press office said in a separate statement, adding that the discussion will center on the strategy in Afghanistan. Petraeus also will meet with British Defense Secretary Liam Fox to talk about Afghanistan, it said.

The initial report on the rescue mission by the troops who carried it out did not mention throwing a grenade, but a follow-up report "raised a lot of questions about what killed" Norgrove, U.S. Navy Capt. Gary Kirchner told CNN after Cameron spoke.

The mission commander called Petraeus as soon as he learned a grenade had been thrown, Kirchner said, without naming the commander.

The investigation will be done "with all due haste," Kirchner said. It will review the mission plan, communications and video from the operation, he said.

A "review of surveillance footage and discussions with members of the rescue team do not conclusively determine the cause of her death," the U.S. military said in a statement Monday.

The British government aims to share as much of the final report as possible with lawmakers, British Foreign Secretary William Hague said Monday.

Cameron said he believed "profoundly" that it had been the right decision to try to rescue her, although he looked shaken at times during his statement to reporters.

The rescue operation was planned and carried out by U.S. Special Forces, Hague told the House of Commons Monday after Cameron spoke.

He personally authorized efforts to rescue her by military action "within a few hours" of her being captured, Hague said. He said intelligence and weather conditions played a role in determining the timing of the operation.

Norgrove, who had been held hostage since late last month, worked for DAI, an agency that provides various services to developing nations.

She spent much of her career managing projects for farmers and rural workers.

Cameron said in a statement Saturday that Norgrove "was doing valuable work for the Afghan people."

Hague said in a written statement Saturday that his forces received information about where she was held and "decided that, given the danger she was facing, her best chance of safe release was to act on that information.

"Responsibility for this tragic outcome rests squarely with the hostage takers," Hague said.

"From the moment they took her, her life was under grave threat. Given who held her, and the danger she was in, we judged that Linda's best chance lay in attempting to rescue her."

Norgrove was being held by two Taliban commanders, Mullah Basir and Mullah Keftan, who were both killed in the raid, an Afghan intelligence official said.

An Afghan official said last month that the British woman, two Afghan drivers and a security guard had been kidnapped after an exchange of gunfire September 26 in the Chawkay district of eastern Kunar province.

Abdul Marjan Adel, a local provincial official, had said that the four were being held in a "very remote area," and that Afghan and international forces were looking for them.

He said they were healthy and located in the Dewcar valley.

The three Afghans kidnapped with Norgrove had been released days ago, according to another Afghan intelligence official and a local provincial government official.

James Boomgard, DAI president and chief executive officer, called the news of her death "devastating" and said his operation is "saddened beyond words by the death of a wonderful woman whose sole purpose in Afghanistan was to do good."

"Linda loved Afghanistan and cared deeply for its people, and she was deeply committed to her development mission. She was an inspiration to many of us here at DAI, and she will be deeply missed."

He was speaking before Cameron's statement about the confusion over the cause of her death.

After Cameron spoke, Boomgard said: "Throughout this ordeal, we were satisfied that both the British and American authorities were doing everything in their power to secure Linda's release. ... We have neither the information nor the inclination to second guess the decisions made."