Nigeria's military is battling an increasingly vicious Islamist insurgency by Boko Haram, which wants to carve an Islamic state out of religiously mixed Nigeria. But its forces frequently come repeatedly under fire for human rights abuses, including torture and extrajudicial killings they usually deny.
It was not possible to independently verify the video, which also includes images of suspects being pulled off the back of trucks and beaten by soldiers and allied civilian militias.
Amnesty said the extrajudicial killings occurred shortly after Boko Haram's attack on a detention centre in Giwa Barracks, in the northeastern city of Maiduguri, on March 14.
Nigerian Defence spokesman Major-General Chris Olukolade, who normally bristles at suggestions of abuses by Nigerian soldiers, said in at statement that "the military authorities view these grave allegations very seriously.
"Much as the scenes depicted in this video are alien to our operations and doctrines, it has to be investigated to ensure that such practices have not crept, surreptitiously, into the system," Olukolade said.
He emphasised that such behaviour would be counter to the training Nigerian troops are given.
"That level of barbarism and impunity has no place in the Nigerian military. Respect for the sanctity of life is always boldly emphasized in our doctrinal training," he said.
In the most gruesome of the videos, suspects are kept to one side while graves are dug. Then the grave is shown half-full of bodies. A half-naked man is pulled from a truck and held down while a man in military uniform slices his neck open with a combat knife, hurling his body into the pit. The scene is repeated with another suspect on the same bloodied patch at the edge of grave.
Amnesty said 4,000 people had been killed in the conflict this year.
A military operation since May last year has aimed to crush the rebels. But they have proved remarkably resilient and have struck back in attacks that increasingly target the civilian population, killing hundreds.
"This shocking new evidence is further proof of the appalling crimes being committed with abandon by all sides in the conflict ... what does it say when members of the military carry out such unspeakable acts and capture the images on film?" said Salil Shetty, Amnesty International's secretary general.
"Numerous testimonies we have gathered suggest that extrajudicial executions are, in fact, regularly carried out by the Nigerian military," she added.
Rights groups argue that such acts by the military are not only wrong but counter-productive, as they fuel much of the anger that has helped drive the insurgency over the past five years. It is also a primary reason cited by U.S. and British forces for not giving Nigeria more counter-insurgency support.
Boko Haram was a largely non-violent clerical movement against Western culture until the killing of its founder, Mohammed Yusuf, in police custody transformed it into a full- scale armed rebellion.
Olukolade said forensic experts would study the footage "in order to ascertain the veracity of the claims with a view to identifying those behind such acts. This will ... stimulate necessary legal action against any personnel or anyone found culpable in accordance with the provisions of the law."
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