MI5 Director General Andrew Parker had been called before the home affairs committee to expand on evidence he gave to lawmakers last month about the intelligence released by the fugitive former US analyst.
However, Home Secretary Theresa May, the interior minister, has written to the committee to decline the invitation, saying she did not believe it was "appropriate or necessary".
Prime Minister David Cameron also declined a request to question his national security adviser, Kim Darroch.
He added: "Ministers should take care not to dictate to parliamentary committees which witnesses can be called and for what reasons.
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"Witnesses, no matter how senior, should not be afraid of answering questions from MPs."
Parker appeared before parliament's intelligence and security committee (ISC) in November, alongside the chiefs of the MI6 external spy agency and the GCHQ listening agency, for an unprecedented televised grilling.
That was sufficient scrutiny, May argued, adding: "I do not believe that it would be appropriate or necessary for the oversight provided by the ISC to be duplicated by another committee."