"There are a number of enquiries, a number of claims, some which may well be substantiated and some which may not be."
Mr Key told The Nation, the Government had straight forward expectations of Serco.
"They are to honour their contract, if they don't, there are potential financial penalties or other penalties.
"Secondly it's actually to keep prisoners safe and the third is actually to make sure that the Ministry of Corrections and therefore the Minister, is kept informed of any issues.
"I expect Serco to meet those obligations and if they don't, well, there will be very serious consequences."
He said as new information came to light, the Government was acting quickly.
"The fight clubs and the claims of those, that video footage emerged Thursday week ago, by Sunday there was a full enquiry, it has got a couple of independent parts to that including the Ombudsman overseeing that."
Mr Key told The Nation he believed the Government had acted "thoroughly and carefully".
"In giving Serco a contract we have very strong expectations of what they should do, I expect them to meet that contract, if they don't meet it, all hell will break loose, including financial penalties.
"We have the advantage through a privately run prison, something we actually don't have in a publicly run prison and that is, we have a contract.
"They have to honour that contract. If they don't honour that contract right through that process there are penalties and remedies available to the Government."
Minister retains support
Embattled Corrections Ministers Peseta Sam Lotu-Iga has the total support of his cabinet colleagues and caucus, Deputy Prime Minister and Finance Minister Bill English told the National Party conference in Auckland today.
"This is team that supports each other," in a speech on the economy.
"We all get our turn in the media and this last week it was Sam and he has the total support of the cabinet and the caucus.
"He is dealing with the challenges of managing New Zealand's most dangerous people in New Zealand's toughest place, Mt Eden Prison and we will support him through that," he said to applause.
Later he said it would be a bit naive to think that dangerous people in Mt Eden do not fight.
"It seems to be regarded as news that there's fights in prison - you know there's fights in 15-year-old rugby teams."
The Department of Corrections yesterday took over the management of the privately-run prison from Serco while investigations are undertaken into allegations about violence against prisoners and possible non-disclosure of violence and injuries.
Labour's Kelvin Davis has suggested that the death of prisoner Nick Evans was related injuries he sustained at Mt Eden.
Mr English told reporters that Mr Lotu Iga was "handling a difficult situation well" and said there were political interests that were "trying to deal to Serco."
He also said that in general the prison system had been running well in the past few years both in the public and private sector.
There had been a greater emphasis put on literacy, work-training, and addiction to reduce the rate of re-offending.
- NZME with additional reporting from Audrey Young
