David Cameron addresses the House of Commons during today's session
Asked by Liberal Democrat MP John Leach whether he would "encourage media organisations to immediately release footage" to aid police investigations, Cameron answered: "I will certainly do that".
"Everyone has a responsibility. The media has a responsibility and I hope they will accept it."
Cameron's comments came during an emergency House of Commons session convened in the wake of four nights of violent rioting across the country.
Fran Unsworth, the BBC's head of newsgathering, was asked on BBC Radio 4's Media Show yesterday whether the broadcaster would be prepared to hand over unused footage to the police.
"No we don't do that without a court order," Unsworth said.
Asked whether the "transparent criminality" of looters meant that the BBC should hand over the footage, she said:
"No. It's a matter of principle for us, we don't just hand over our rushes to the police without going through a proper process which is via the courts.
"It doesn't matter what the nature of the offences are, and if we went down the route of making judgments about the nature of offences, that would compromise our editorial standards.
"It is a matter for a court to decide whether it's criminal or not, not for us to decide ... It doesn't matter what I think about whether it's criminal or not. These people will probably be picked up by police who will seek to take our rushes from us.
"If they come up with a court order we will probably hand them over because that's the process and the court will decide whether its criminal activity or not. But we are not in a position to prejudge that."
Responding to Cameron's comments, a spokesman for the BBC said today: "We have standard processes in place to deal with requests from the police through our litigation department, regardless of the subject matter. Any request would need to be dealt with by the courts."
ITN, which produces ITV News and Channel 4 News, echoed the BBC's statement: "We expect any request will come from the police. When that happens, we will deal with it as per our established practice for handing over unbroadcasted material."
Cameron also said, during a prepared statement, said that the government was considering banning people from social networks if they are thought to be using them to organise rioting.
"Everyone watching these horrific actions will be struck by how they were organised via social media. Free flow of information can be used for good. But it can also be used for ill. And when people are using social media for violence we need to stop them."
Cameron said that the government was working with the police, intelligence services and industry "to look at whether it would be right to stop people communicating via these websites and services when we know they are plotting violence, disorder and criminality".
Police have been monitoring Twitter and Blackberry Messenger during the latter stages of the rioting and several people have been arrested on suspicion of inciting violence on those networks.