|Cameron, right, raised the case of Lina Norgrove during a meeting in London with Petraeus, left [EPA]
General David Petraeus, the top US general in Afghanistan, is said to have vowed to make the investigation into the recent death of a UK aid worker in Afghanistan a "personal priority".
Petraeus made the pledge after David Cameron, the British prime minister, raised the case of Linda Norgrove, who died during an attempt by US forces to rescue her, during a meeting on Thursday.
Earlier this week, the prime minister revealed that Norgrove, a kidnapped British aid worker, may have been killed by her American rescuers, rather than her Taliban captors as first reported.
A statement from Cameron's office indicated that Petraeus told the prime minister that the investigation was "a personal priority" and promised that there would be full co-operation between the US and Britain.
Nato initially had said Norgrove died when her captors detonated a bomb as US forces moved in to free her.
But it later emerged that she may have been killed by a grenade thrown by US troops, with new details suggesting that the US special forces soldier believed to be responsible failed to see that she had broken away from the kidnappers.
Britain's Guardian newspaper reported that Norgrove was lying in a foetal position to keep safe when a US grenade was thrown during an attempt to rescue her last week.
The Guardian reported that the US soldier could face disciplinary action, citing sources in London and Kabul.
It said the soldier failed to inform his commanding officers that he had thrown the explosive until long after the event.
The incident comes at a critical moment for US and Nato forces, with reports that top Taliban leaders may be willing to sit down for talks with the US-backed government in Afghanistan as a step to ending the nine-year war.
With Britain's defence review to be announced next week, Petraeus is also likely to have sought reassurance about the impact of cuts at the defence ministry on the UK's role in Afghanistan.
The statement from Cameron's office said Petraeus told Cameron that there had been progress in Afghanistan and said that operations in Kandahar and Helmand Province were proceeding well.
The two agreed that training the Afghan national security forces remained the top strategic priority.
"The prime minister confirmed that 320 British troops would be redeployed in training roles following the changes to force laydown in Helmand, to help accelerate the training effort," the statement said.
In Brussels on Thursday, Robert Gates, the US secretary of defence, declined to answer questions about Norgrove's death because the investigation is still ongoing.
But he said the Taliban were to blame for the kidnapping that led to her death.
"I think there is an important point to be made here: Let's not forget who put her in harm's way, who kept her in a mountain side at 8,000 feet. So this is a terrible tragedy but the Taliban bear the principle responsibility for this," he said.