The US/UK investigation into the failed rescue of British hostage Linda Norgrove should have no time limit on it, William Hague has told the BBC.
The foreign secretary said the top priority was to find out what happened.
Mr Hague will discuss the inquiry with top US commander in Afghanistan, Gen David Petraeus, in London this week.
Ms Norgrove's death was at first blamed on her captors but it was then said a US grenade might have killed her. The US now says it is keeping an open mind.
Investigators in the US said the British aid worker could have been killed by a Taliban weapon or a US one, or a combination of both.
Meanwhile Downing Street has announced that Brigadier Rob Nitsch will be the senior British representative on the joint US/UK investigation panel.
US President Barack Obama has offered his deepest condolences over the death in a call to Prime Minister David Cameron.
In a BBC interview Mr Hague also acknowledged it had been embarrassing to have to admit he had released wrong information about how Ms Norgrove died, but insisted it was still right to pass it on to the public.
"I think when we are told something in good faith we must tell the country that information in good faith. Of course it can turn out subsequently to be wrong but that's better than hiding any information.
"We have always erred on the side of transparency in the current government and this is one indication of that," he said.
'Examination of detail'
Gen Petraeus ordered the investigation on Monday after a review of the operation launched to try to free Mrs Norgrove ended in her death on Friday.
His team said they would wait for the investigation to reach a conclusion before making any major statements.
Brigadier Nitsch, the Head of Joint Force Support, UK Forces Afghanistan, will serve alongside the senior US investigating officer Major General Votel on the investigation panel.
Peter Ricketts, the prime minister's national security adviser, will also discuss the operation with the Head of US Central Command in Afghanistan, General Mattis, when the general is in London on Wednesday.
Mr Hague said the length of the inquiry was "really up to the investigators".
"They will have to interview the people involved, they will have to look at the video footage of what happened, so there is quite a bit of examination of detail to go on here.
"I don't think it's for me to set a time limit to that. We're interested not so much in the timing, as in really finding out what happened and why."
Mr Hague said he had "given the green light" to a military operation to rescue Ms Norgrove within hours of her kidnap.
When President Obama spoke to the UK prime minister, he said Ms Norgrove's work represented her extraordinary commitment to advance the lives of others.
Mr Obama and Mr Cameron agreed the rescue mission was necessary because her life was in grave danger.
Nato sources in Afghanistan initially claimed that she had died when one of her captors set off a suicide bomb but it then emerged she might have been killed by an American grenade.
US military sources said surveillance of the operation from overhead and on the ground was conflicting.
The investigators will look at surveillance footage of the operation taken by helicopters or pilotless drone aircraft as well as from cameras mounted on the helmets of the soldiers on the ground.
At a Downing Street news conference on Monday, Mr Cameron said 12 meetings of the government emergencies committee, Cobra, had taken place before Foreign Secretary William Hague and the US agreed the rescue attempt should go ahead.
The decision was then approved by the prime minister.
Ms Norgrove, 36, from the Isle of Lewis, was employed by US aid group DAI. She was seized in the Dewagal valley in Kunar province on 26 September.
Three local staff, who were kidnapped with her when the two cars they were travelling in were ambushed, were released unharmed last week.
DAI vice-president Betsy Marcotte told BBC Radio 4's Today programme she did not blame US troops for her colleague's death.
"Clearly it is distressing news, but it doesn't change anything for me," she said.
"I feel confident in how this was handled and that we have been satisfied that the British and the Americans were doing everything they could."