He said some of the international reporting on the incident was incorrect.
"We know that the men who appear in this video are not prisoners who escaped from Naboro last year. We have already established this,'' he said.
Mr Sokomuri said the procedure of investigation police would follow was similar to those followed when complaints had been lodged against police officers in other jurisdictions such as Australia, South Africa, USA and New Zealand.
He said they were not prepared to speculate on the identities of those involved, so as not to prejudice the investigation.
The video has appalled human rights activists here, who are calling on the Government to lean on the interim Fiji Government to take action over the video.
Human rights campaigner and lawyer Peter Williams QC, said New Zealand aid could be withheld from Fiji if no charges were brought against the perpetrators of the alleged torture and beatings.
"I think we're waiting in New Zealand to see what the authorities are going to do about it. If no charges are brought then I think the New Zealand Government should bring some pressure on the dictatorship over there, the military government, to do something about it.''
The video showed "shocking brutality'', Mr Williams said.
"The government over there, the police force, the military, they've got to do something about it otherwise the reputation of Fiji will go down like a piece of lead through water.''
Prime Minister John Key is expected to comment on the issue from South America tonight (NZT).
Amnesty International was also investigating the video.
It's executive director Grant Bayldon said they have a team in London working on verifying the video.
"This appalling incident appears to be the latest example of abuse by the military. The Fijian authorities must treat this shocking footage with the utmost seriousness and immediately initiate an independent investigation,'' said Mr Bayldon.
"While the video is still to be verified, what is clear is that torture is unacceptable under any circumstances and those responsible must be brought to justice.''
Mr Bayldon said the humiliation of the men, and their injuries, were "very serious".
"Forced to undress and harassed by a dog, as men nearby laugh, it is difficult to watch. The subsequent brutal beating with batons is harrowing. It is torture.''
The video showed the beatings being administered by plain-clothed men speaking Bauan - a Fijian dialect.
It was thought the footage was from an incident last year where five prison escapees were apparently assaulted by the military when the inmates were eventually recaptured.
