The Chief of Defence Force, Lieutenant General Rhys Jones said the families of all other SAS soldiers in Afghanistan had been contacted and told that their men were still alive.
No other New Zealanders were injured in the attack.
Mr Jones said it was too early to say when the soldier's body would be returned. His funeral was likely to be closed due to his role with the SAS.
His colleagues in Kabul would not be returning for the funeral, however it was intimated that other SAS members would attend the service.
At a press conference yesterday Mr Key confirmed the soldier's death with "great sadness and a heavy heart".
"I believe that New Zealand will take the loss of this SAS soldier very badly," he said.
"We highly value the work that they do... and the courage and bravery that they show."
Mr Key said he was "deeply saddened" by the death. But he stood firm on his decision to have a New Zealand presence in Afghanistan.
"I believe passionately in the work that they are doing. They are ensuring that the innocent lives of thousands in Afghanistan are preserved, and giving Afghanistan hope for their country.
"They are working to make the world a safer place from global terrorism. It is not my view that due to the death of our soldier, we should reconsider our position in Afghanistan. We stay absolutely committed to continuing our work in Afghanistan.
"It would be the completely wrong thing for us to consider cutting and running. I don't think it would honour the death of this soldier and I don't think it would actually be what New Zealanders would expect us to do in this situation."
Mr Jones said all SAS member and their families knew the dangers of working in Afghanistan.
"In the military there's always the reality of death in operation or death in training. It's always a reality. Everyone who goes to Afghanistan knows there's a probability of death."
He said military families were also realistic about the dangers.
Mr Jones said there had been an expectation that there was a "probablity" of a terrorist attack in Kabul yesterday, on the anniversary of Afghanistan's independence from Britain.
He said that expectation and other information, which he would not be drawn on, meant the SAS was on high alert.
Defence Minister Wayne Mapp said the soldier's death would be keenly felt by his comrades in the SAS.
A full debrief had been held in Kabul and SAS members had "consoled each other" but were now back to work.
"Our soldiers are serving our nation to protect our nation from international terrorists. The SAS are amongst the bravest and most resourceful of our soldiers," he said.
"They are resourceful and resilient. This is a particularly sad day."
NZ Army combat deaths since 1990:
* 24 July, 2000: Private Leonard Manning, in East Timor.
* 4 August, 2010: Lieutenant Tim O'Donnell, in Afghanistan.
* 19 August, 2011: Unidentified SAS soldier, in Kabul.