London, England (CNN) -- The top U.S. military commander in Afghanistan, Gen. David Petraeus, met British Prime Minister David Cameron Thursday in the wake of a failed operation to rescue a British aid worker from kidnappers in Afghanistan.
Petraeus told Cameron the investigation into the death of Linda Norgrove was "a personal priority for him," Cameron's office said in a statement after the meeting.
She may have been killed by a grenade thrown by American forces trying to free her, Cameron said Monday -- after British and NATO officials said earlier that her kidnappers had killed her.
The meeting between the general and the prime minister is not a response to the rescue that went wrong.
"It's a long-standing meeting and has been in the diary for a number of weeks," the Downing Street press office said this week, adding that the discussion would center on the strategy in Afghanistan.
Petraeus also will meet with British Defense Secretary Liam Fox to talk about Afghanistan while he is here, Cameron's office said.
Cameron said during Prime Minister's Question Time in the House of Commons on Wednesday that early information about Norgrove's death over the weekend "most likely was wrong."
"This investigation is now under way," he said. "When there is new information to bring to the House, we will bring it to the House."
The investigation will be led by a senior officer from U.S. Central Command, an International Security Assistance Force official told CNN this week.
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.
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.
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 this week.
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.
Cameron said he believed that it had been the right decision to try to rescue her.
"It is an impossibly difficult decision to make about whether to launch a raid and try to free a hostage," he said. "In the end we must all be clear: the responsibility for Linda's death lies with those cowardly, ruthless people who took her hostage in the first place."
The rescue operation was planned and carried out by U.S. Special Forces, British Foreign Secretary William Hague told the House of Commons Monday.
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.