The Intelligence and Security Committee (ISC) has called on the public to provide written and oral evidence, as it seeks to determine whether current legislation on the privacy of communications is still "fit for purpose".
In July, the ISC said it would investigate allegations that British spy agency GCHQ illegally tapped global internet traffic and phone calls, and then shared this intelligence with its US counterpart, the National Security Agency (NSA).
Its snap investigation into the GCHQ's Tempora programme and its links to the US PRISM programme concluded that the allegations were "unfounded" and that GCHQ had not circumvented or attempted to circumvent UK law.
It said that its next step was to consider whether the current statutory framework governing access to private communications remains adequate given the developments in IT since it was enacted.
The chairman of the ISC, Sir Malcolm Rifkind, said that concern had been expressed at the suggested extent of the capabilities available to the intelligence agencies and the impact upon people's privacy "as the agencies seek to find the needles in the haystacks that might be crucial to safeguarding national security".
"There is a balance to be found between our individual right to privacy and our collective right to security. An informed and responsible debate is needed," he said.
Rifkind said that the committee would be looking at classified information that only the ISC had access to, but would also be inviting written evidence more broadly - including from the general public.
"Once [the ISC] has considered those written submissions it will also hold oral evidence sessions, some of which it expects to hold in public," he explained.
The ISC claims it is "not a committee of parliament", and that it reports directly to the Prime Minister, David Cameron.
The ISC, which is made up of parliamentarians selected by the Prime Minister, oversees the intelligence and security activities of the UK, including the policies, expenditure, administration and operation of the MI5, MI6 and GCHQ, among other bodies in the UK intelligence community.
It has, in the past, been highly critical of the UK's cyber security efforts. In July 2011, it said that the government had shown "confusion and duplication of effort" in its approach to cyber security, and last year it suggested that UK cyber security was inadequate and needed work.