The commander of international forces in Afghanistan has said finding out how kidnapped British aid worker Linda Norgrove died is his "priority".
Downing Street reported General David Petraeus's comments after he met Prime Minister David Cameron in London.
It was first thought that Miss Norgrove was killed by her captors during the US rescue mission, but evidence suggests it may have been a US grenade.
The Foreign Office said her body was repatriated to the UK on Thursday.
A joint US/UK military inquiry will examine exactly how she died.
A Downing Street spokesman said: "General Petraeus said that the investigation was a personal priority for him and emphasised that there would be full co-operation between the US and UK."
Gen Petraeus's visit was arranged before Miss Norgrove was killed last week during a US special forces rescue attempt sanctioned by Mr Cameron.
He and ambassador Mark Sedwill, Nato's senior civilian representative in Afghanistan, are due to address think tank Royal United Services Institute later about the international mission in Afghanistan.
The general is likely to face several questions about the death of Ms Norgrove when he speaks to the media at the event.
The prime minister's office announced on Wednesday that a British coroner would oversee a post-mortem examination on her body.
Speaking at Prime Minister's Question Time, Mr Cameron said he had stressed to US President Barack Obama that it was "extremely important" there should be a joint US/UK investigation.
That inquiry is being led by Brigadier Rob Nitsch, the Head of Joint Force Support, UK Forces Afghanistan and senior US investigating officer Major General Joseph Votel.
Speaking at a news conference in Brussels, the US Defence Secretary Robert Gates said the Taliban put Miss Norgrove in harm's way when they kidnapped her.
"The death of this aid worker is a tragedy and we offer condolences to her family and friends," he said.
"But I think there's also an important point to be made here. Let's not forget who put her in harm's way, who kidnapped her and who kept her on a mountainside at 8,000 feet.
"So, this is a terrible tragedy but the Taliban bear the principal responsibility here."
BBC security correspondent Frank Gardener says Whitehall officials insist there is no animosity between the US and UK governments over Miss Norgrove's death, just a determination to establish exactly how it happened.
But reports have been emerging, unchallenged by senior British officials, that Miss Norgrove was most probably killed by a grenade thrown by a US Navy Seal commando as she crouched down in the dark after escaping from her captors during the rescue mission, our correspondent adds.
Gen Petraeus was also expected to discuss the UK's defence review, due to be announced next week.
Foreign and defence ministers of Nato member countries have been meeting in Brussels to consider changes to the alliance's strategy.
Issues like missile defence and nuclear disarmament are on the agenda, as Nato seeks to adapt itself to new security challenges against the backdrop of Afghanistan.