The PM raised the issue during a meeting in Downing Street with General Petraeus, commander of NATO forces in Afghanistan.
Earlier this week, Mr Cameron announced that a full UK/US investigation will be launched into Ms Norgrove’s death after it emerged she may have died as a result of a grenade used by US forces during an operation to rescue her from Taliban forces.
Following the meeting, a Downing Street spokesperson 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.
During the meeting, General Petraeus also updated the PM on progress in Afghanistan and said that operations in Kandahar and Helmand Province were proceeding well.
They agreed that training the Afghan National Security Forces remained the highest strategic priority for the military campaign, given the need to get the Afghan Government to take responsibility for its own security.
A Downing Street spokesman said:
The Prime Minister confirmed that 320 British troops would be redeployed in training roles to help accelerate the training effort. General Petraeus thanked the PM for the ongoing British commitment to Afghanistan and for the valued contribution made by British troops, civilians and equipment.