The White House has said that it welcomes media interest in US surveillance practices, despite confirming that the Department of Justice is in the early stages of a leak investigation that may lead to criminal prosecutions of whistleblowers who revealed them.

As the second of two secret US monitoring programmes was partially declassified in response to leaked disclosures this week, officials speaking at a presidential summit in California told the Guardian that the ensuing public debate was necessary.

Deputy national security adviser Ben Rhodes said: "The debate that's been sparked by these revelations – while we do not think that the revelation of secret programmes is in the national security interest of the US – the broader debate about privacy and civil liberties [is something Obama] went out of his way to identify as one of the trade-offs we have to wrestle with.

"We'll have that debate. We welcome congressional interest in these issues, we welcome the interest of the American people and of course the media in these issues but we feel confident we have done what we need to do strike a balance between privacy and security by building in rigorous oversight mechanisms."

His comments follow a decision late on Saturday by the intelligence community to declassify parts of its Prism programme – revealed by the Guardian and the Washington Post on Thursday – so that it could explain how its collection of data from internet companies was supervised by Congress.

The statement confirmed that Prism was "an internal government computer system used to facilitate the government's statutorily authorised collection of foreign intelligence information from electronic communication service providers under court supervision".

Director of national intelligence James Clapper said the Guardian and Washington Post had failed to adequately convey how much constitutional oversight the programme received. "Over the last week, we have seen reckless disclosures of intelligence community measures used to keep Americans safe," he said in a separate statement. "In a rush to publish, media outlets have not given the full context, including the extent to which these programmes are overseen by all three branches of government to these effective tools."

But the question of how effective such oversight has been was brought into question this weekend by growing numbers of congressmen, who claim they had not been made aware of the Prism programme or an earlier disclosure by the Guardian of court orders forcing phone companies to hand over US phone records.

And Obama's chief national security adviser, Tom Donilon, was forced to reject suggestions that the oversight process had been undermined because data was being withheld from Congress.

This followed the disclosure of a third programme by the Guardian, codenamed Boundless Informant, that appeared to contradict recent assurances given to Congress that there was no record of how much data was gathered from US computers.

"These programmes are very important to the United States and its ability to protect itself," Donilon told the Guardian in response. "They are subject to very careful procedures to ensure particularly that privacies and civil liberties are protected, but are also subject to very careful oversight by a court and careful and persistent oversight by the Congress."

Officials in Washington have yet to make their mind up to how to respond to the leaks to the Guardian and other newspapers, particularly after a storm of protest followed the surveillance of phone records belonging to Associated Press reporters in pursuit of other leaks.

"What we are focused on [now] is doing an assessment of the damage that is being done to US national security by the revelation of this information, which is necessarily secret because we need to be able to conduct intelligence activities without those methods being revealed to the world," said Rhodes.

"As relates to any potential investigations, we are still in the early stages of this. This is something that will be addressed by the Justice Department and intelligence community in the coming days in consultation with the agencies that have been affected by these very disturbing leaks of national security."