Senior members of the coalition are at odds over Britain's intelligence agencies after Downing Street dismissed a claim by Vince Cable that Britain arguably lacks a proper system of oversight.

As the business secretary praised the Guardian for performing a considerable public service in publishing leaked documents from the US National Security Agency, No 10 said David Cameron was satisfied with the current system of oversight. But the prime minister's spokesman added that members of the national security council, of which Nick Clegg is a member, were entitled to question the intelligence agencies.

The spokesman said: "There is a debate that is outside of government that is often reported in [the Guardian] and other newspapers. There is the scope for members of the national security council, privy councillors, to ask questions and the like to better understand the work that the agencies do. That is always open to them."

Downing Street moved to clarify Cameron's thinking after Cable confirmed that Clegg was setting in train an examination of the oversight of Britain's intelligence agencies.

The business secretary said the Guardian had made the "entirely correct and right" and courageous decision to publish details from secret NSA files leaked by the US whistleblower Edward Snowden. He said that arguably Britain did not have proper oversight of the domestic intelligence service MI5, its overseas agency MI6 and the eavesdropping centre GCHQ.

Cable's views were given short shrift by Downing Street. The spokesman pointed out that the prime minister had said on Thursday: "If people want to suggest improvements about how they are governed and looked after I am very happy to listen to them, but as far as I can see we have a very good system."

Asked whether the government was setting up a review into the oversight of the agencies, the spokesman said: "There is not a government review in the way that you described – correct. There is no government review."

Aides to Clegg told the Guardian on Thursday that the deputy prime minister would start conversations in government about how to update the legal oversight of the UK's security services in the light of disclosures by the Guardian that powerful new technologies appear to have outstripped the current system of legislative and political oversight.

The aides said he would be calling in experts from inside and outside Whitehall to discuss the implications of the new surveillance technologies for public accountability and trust. It is the first time such a senior figure in government has conceded that the revelations published in the Guardian have highlighted concerns about the accountability of the security services.

Cable, who reserved judgment on Snowden's decision to leak the files, confirmed the Guardian report about the Clegg plan. He told the Today programme on BBC Radio 4: "I think the Guardian has done a very considerable public service. Mr Snowden's contribution is two-fold. One is a positive one, which is whistleblowing, and the other is more worrying, that a large amount of genuinely important intelligence material does seem to have been passed across.

"The conclusion which Nick Clegg came to, and set out this morning, is that we do need to have proper political oversight of the intelligence services and arguably we haven't until now. What they [the Guardian] did was, as journalists, entirely correct and right. Mr Snowden is a different kettle of fish."

The business secretary later dismissed as "frankly somewhat bizarre" a claim in the Times by Sir David Omand, the former head of GCHQ, that the Snowden leaks had inflicted more damage than the Soviet Union's Cambridge spy ring. Cable told BBC News: "I mean, they were acting covertly over a long period of time. This was a whistleblower acting very publicly. There is a question about sensitive intelligence he put into the wrong hands. That will obviously have to be pursued."

Asked whether there was a distinction between the decision to leak the information and the right to publish it, Cable replied: "I think there is a distinction between whistleblowing to draw the public's attention to things happening in the intelligence world that shouldn't have been happening – absolutely right – and actually putting into the hands of other people a lot of very, very detailed intelligence information which they shouldn't have had. I think it is an important distinction and I think most people would understand that."

Clegg first hinted at his plans to start conversations in government in his weekly phone-in on London's LBC radio, saying: "I think it is right to ask whether there is anything more we can do to make sure the public feel accountability is working in this area properly. There is a totally legitimate debate about the power of these technologies, about how you get the balance right, how you do make sure these technologies are used in an accountable and proportionate way."

But Clegg also joined Cameron and the head of MI5, Andrew Parker, in declaring that the Guardian had published information, passed to the paper by Snowden, that was not in the public interest. "I don't think just giving technical secrets to those who wish to do us harm serves any purpose."

Clegg's aides did not give specific examples of details published by the Guardian that would give this help to terrorists.

Cameron said: "When you get newspapers who get hold of vast amounts of data and information that is effectively stolen information and they think it's OK to reveal this, I think they have to think about their responsibilities and are they helping to keep our country safe."