Transparency International New Zealand has added its name to those calling for an inquiry, with its chief executive Janine McGruddy saying that by welcoming an inquiry the NZDF "would grow the public's trust, not lessen it".
When English was asked yesterday how Keating, a former commanding officer of the NZSAS, was independent, he said Keating was not involved in the raids, dubbed Operation Burnham.
However Little said he didn't agree with that view.
"No, he is the Chief of Defence Force. He has a set of interests to protect, and I think that was wrong to call Tim Keating as the Chief of Defence Force somehow independent of the force that is conducted this mission that has caused controversy."
In a letter to Defence Minister Gerry Brownlee on Friday, Keating said under the Armed Forces Discipline Act 1971 there were three forms of inquiry available to him as Chief of the Defence Force within the military jurisdiction, and after his review of Operation Burnham he did not consider an internal inquiry was needed.
Keating noted that his decision did not preclude another authority inquiring into the claims, for instance, the New Zealand Police.
The Inquiries Act 2013 allows for public and government inquiries for the purpose of inquiring into, and reporting on, any matter of public importance.
Lawyer Graeme Edgeler said an inquiry under the Inquiries Act could require members of the NZDF to give evidence, although some may be able to decline if they are worried it might incriminate them.
Edgeler said a police investigation cannot require people to be interviewed, but could obtain search warrants or production orders.
Other possibilities for further investigation included an inquiry by Parliament's Foreign Affairs and Defence Committee, Edgeler said, and allegations in Hit & Run that a prisoner had been beaten by an SAS member and later tortured after being handed to Afghan authorities could potentially be investigated by the Chief Inspector of the Crimes of Torture Act.
Little said he believed an inquiry could be headed by a retired High Court judge or similar, and parts of the inquiry could be conducted behind closed doors if information needed to remain classified.
English said yesterday the classified video he saw confirmed the "extensive steps, restraint and care" that forces took to minimise the chances of civilian casualties.
The Prime Minister would not go into detail about what the footage showed and said it would not be publicly released. He did not watch footage of the whole operation but was confident in what he saw.
"There are a number of different points of view from a number of different aircraft."
English said he had become more convinced after reviewing material that Keating's conclusion that there was no misconduct was right.
He had not spoken to anybody outside the NZDF in reaching that conclusion, but denied the NZDF had investigated itself, saying the raids had been investigated by the International Security Assistance Force (ISAF).
Hit & Run by journalists Nicky Hager and Jon Stephenson claims six civilians were killed and 15 were injured in the 2010 raids, and those facts have been covered up by the NZDF.
The book said the raid was a revenge attack on insurgents who were believed to be responsible for the death of soldier Timothy O'Donnell, the first New Zealand combat death in Afghanistan.
Stephenson and Hager, Labour, the Green Party, New Zealand First, United Future and former Defence Minister Wayne Mapp have all called for an inquiry into the Hit & Run allegations, as have lawyers acting for Afghan villagers.
Keating and the NZDF say the book contains major inaccuracies, including the location of the villages where the raids took place, named in the book as Naik and Khak Khuday Dad.
Nine insurgents were killed in the raids and it was possible civilians died because of misfire from a US helicopter, Keating said last Monday, but this could not be established.
The NZDF has previously said investigations by ISAF after the raids determined allegations of civilian deaths were "unfounded". Asked if that was misleading, English said yesterday he understood it was a legal term.
