Cameron's comments were the highest profile intervention by a British official in a debate about whether the left-leaning daily was right to publish Snowden's revelations about US and British spy programmes.
"I think the plain fact is that what has happened has damaged national security," Cameron told parliament.
"And in many ways the Guardian themselves admitted that when they agreed -- when asked politely by my national security adviser and cabinet secretary to destroy the files they had -- they went ahead and destroyed those files.
Cameron was replying to a question by former defence secretary Liam Fox, who said it was "bizarre" that "the hacking of a celebrity phone demands a prosecution, but leaving the British people and the security personnel more vulnerable is 'opening a debate'?"
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The Guardian has strongly defended the Snowden leaks, which it began publishing in August. It says the publication has opened a debate about secrecy and freedom of speech.
But several current and former British officials have warned in recent days that the details leaked by Snowden are harmful to Britain's security.
The newspaper said in August that experts from Britain's electronic eavesdropping centre GCHQ had on July 20 supervised the destruction of the hard drives and memory chips on which its Snowden material had been saved.
The government has confirmed that Cameron's most senior policy advisor, Cabinet Secretary Jeremy Heywood, was sent to tell the Guardian they had to either destroy or return the material, or face legal action.
Glenn Greenwald, the Guardian reporter who broke many of the Snowden stories, said Tuesday he is leaving the newspaper for an unspecified "dream" project.