In a statement, a spokesman for deputy prime minister Nick Clegg, gave the first official confirmation that the cabinet secretary Jeremy Heywood made the request to the Guardian.
The intervention by Clegg came after Yvette Cooper, a Labour Party politician, said that parliament's intelligence watchdog should investigate Cameron's role in asking the Guardian to surrender or destroy the National Security Agency documents leaked by whistle-blower Edward Snowden.
The shadow home secretary made her call after the Independent reported that Heywood made the request to the Guardian on the instructions of the prime minister.
Keith Vaz, the Labour chairman of the Commons home affairs select committee, was quoted as saying by the Guardian that the prime minister must make a statement to MPs when parliament returns next month.
In a statement issued after the official confirmation that Heywood asked the Guardian to delete its hard drives, Vaz said: "The actions of the cabinet secretary are unprecedented and show that this issue has reached the highest levels of government."
"Although I am very surprised at this revelation it explains why Downing Street, the White House and the home secretary were briefed in advance about David Miranda's detention," the Indian-origin MP said.
A spokesman for Clegg made clear that Heywood was acting on the authority of both the prime minister and his deputy.
"We understand the concerns about recent events, particularly around issues of freedom of the press and civil liberties. The independent reviewer of terrorism legislation is already looking into the circumstances around the detention of David Miranda and we will wait to see his findings," the spokesman said.
"On the specific issue of records held by the Guardian, the deputy prime minister thought it was reasonable for the cabinet secretary to request that the Guardian destroyed data that would represent a serious threat to national security if it was to fall into the wrong hands," he said.
"The deputy prime minister felt this was a preferable approach to taking legal action. He was keen to protect the Guardian's freedom to publish, whilst taking the necessary steps to safeguard security," the spokesman said.
Alan Rusbridger, the editor of the Guardian, had disclosed on Monday night that a "very senior government official claiming to represent the views of the prime minister" asked him to return or destroy all the NSA documents leaked to the paper.
The Guardian agreed to destroy two hard drives last month in the presence of two security experts from Britain's GCHQ eavesdropping centre after the government threatened to take legal action.
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