Yvette Cooper, the Shadow Home Secretary, has called for Westminster's intelligence watchdog to investigate the extent of Mr Cameron's involvement after it emerged he had directed Sir Jeremy Heywood, the Cabinet Secretary, to contact the Guardian.
Keith Vaz, her Labour colleague who chairs the Commons Home Affairs Committee, demanded the PM make a full statement to MPs when they return to Westminster next month given No 10's direct intervention.
This came to light following the detention at Heathrow Airport under counter-terrorism laws of David Miranda, the partner of Guardian journalist Glenn Greenwald, who has worked with Mr Snowden, a former US National Security Agency worker, on a series of security services exposes.
Yesterday, Mr Cameron's colleagues came out to defend his actions.
Nick Clegg, it emerged, had agreed to the move against the Guardian on the understanding that destruction of the classified material would not impinge on its ability to publish articles.
A spokesman for the Deputy Prime Minster said: "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."
William Hague, the Foreign Secretary, said: "The Government clearly has a duty if information is held insecurely and could be damaging to our national security to try to make sure that it is recovered or destroyed. It's a very simple matter."
But Ms Cooper suggested the Intelligence and Security Committee (ISC) should now look at the Coalition's move against the Guardian.
"We don't know what was on the (hard drives) or what the material was that the Government was pursuing.
"However, this may be another area where an inquiry by the ISC may be the way forward in terms of this case."