Sebag-Montefiore said vivid accounts of the battle from New Zealand officers detailed their approach, which was inspired by the fiery words of a Scottish major.
"[They were told] we don't want prisoners, we have to feed prisoners. What we have to do is kill prisoners, the only good German is a dead German."
The actions of the New Zealand fighters, "even in war", amounted to "little more than brutal murder", Sebag-Montefiore said.
Sebag-Montefiore makes the claims in his book Somme: Into the Breach, which is the result of new research from archives, libraries and Red Cross files. It includes first-hand accounts from soldiers, photographers and diary-writers.
RSA national president Barry Clark said he would investigate the accusation but he could not rule out that it might have happened.
Clark said while he didn't feel qualified to comment on the claim, he could not write it off.
"In the sorts of conditions they were serving under with the stresses and strains that people endure during the war, and with how they were prepared for battle... you'd have to have been there to understand what was going on."
He said the trauma of war had a massive impact on soldiers.
"In my opinion the human mind was never designed to understand what was going on around them. You're standing there and your boyhood friend is suddenly blown away by a bomb, by a shell, lost half his face, the mind must have gone through quite a spin. And you don't know how people react under those conditions."
Clark said he could not say without doubt the alleged war crimes did not happen because he was not there.