In his first major speech, Andrew Parker suggested The Guardian's recent disclosures based on information from fugitive former intelligence worker had been damaging to national security.
Mr Snowdon revealed the Cheltenham facility had accessed fibre-optic cables carrying huge amounts of internet and communications data which it shared with the Americans.
Mr Parker told the Royal United Services Institute that the "margin of advantage" the security services enjoyed over terrorists was being eroded by newspaper reporting.
He added: "Reporting from GCHQ is vital to the safety of this country and its citizens. GCHQ intelligence has played a vital role in stopping many of the terrorist plots that MI5 and the police have tackled in the past decade."
He dismissed the notion that his spies monitor "everyone and all their communications" as "utter nonsense".