Any requests by GCHQ for access to British citizens' emails through a controversial US internet monitoring programme would need proper legal authority, potentially including the personal approval of a minister, the chairman of the committee monitoring the UK's spies said.
Sir Malcolm Rifkind said "some intrusion on privacy" was necessary to protect the public, but British intelligence agencies would normally need ministerial authority for access to information about UK citizens.
Foreign Secretary William Hague, the minister responsible for GCHQ, will face questions from MPs later today following a string of revelations about the US government's Prism programme.
The whistleblower who exposed the Prism system condemned the US government's attempts "to destroy privacy, internet freedom and basic liberty".
Details about the programme, and GCHQ's links to it, emerged in The Guardian newspaper following a leak by a former technical worker at the CIA and National Security Agency (NSA).
Edward Snowden, 29, an American IT administrator for the defence contractor Booz Allen Hamilton, revealed his identity at his own request, the newspaper said.
Mr Snowden, who fled to Hong Kong, said: "I can't allow the US government to destroy privacy, internet freedom and basic liberties. My sole motive is to inform the public as to that which is done in their name and that which is done against them."
Prism is said to give the NSA and FBI easy access to the systems of nine of the world's top internet companies, including Google, Facebook, Microsoft, Apple, Yahoo and Skype.
The row crossed the Atlantic after documents emerged suggesting British eavesdropping agency GCHQ had access to the system since at least June 2010.
Tory former foreign secretary Sir Malcolm, chairman of the Intelligence and Security Committee, said GCHQ would need authority for any request to monitor the emails of a UK citizen, even if the surveillance was carried out by the US agencies.
Sir Malcolm told BBC Radio 4's Today programme: "The law is actually quite clear: if the British intelligence agencies are seeking to know the content of emails by people living in the UK, then they actually have to get lawful authority. Normally that means ministerial authority.
"That applies equally whether they are going to do the intercept themselves or whether they are going to ask somebody else to do it on their behalf."
Sir Malcolm said that "in order to protect the public that does require, as President Obama said in Washington, some intrusion on privacy in certain circumstances".
But he added: "It requires ministerial authority or authority from the relevant senior person. It cannot simply be done by the agencies making their own decision about whose mail they are going to intercept or telephone calls they are going to intercept."
Mr Hague, who is due to make a statement on the allegations in the Commons later, said the law-abiding British public had "nothing to fear" from the work of GCHQ.
Mr Hague told BBC1's Andrew Marr Show yesterday: "As someone who knows GCHQ very well... the idea that in GCHQ people are sitting working out how to circumvent a UK law with another agency in another country is fanciful. It is nonsense."
The Cabinet minister declined to confirm that he had personally authorised engagement with the US Prism programme.
But he said checks in place in this country, including reviews of decisions by the Interception Commissioner, were strong.
"That legal framework is strong, that ministerial oversight is strong," he said.
"The net effect is that if you are a law abiding citizen of this country going about your business and personal life you have nothing to fear about the British state or intelligence agencies listening to the content of your phone calls or anything like that.
"Indeed you will never be aware of all the things that these agencies are doing to stop your identity being stolen or to stop a terrorist blowing you up tomorrow."
Shadow foreign secretary Douglas Alexander told Today it was "vital" that the public had confidence that the security and intelligence services were "operating within a framework of accountability and legality".
He said Mr Hague "does need to seek to give assurances to Parliament about the laws and procedures that are in place, in particular in relation to our vital information-sharing relationship with the United States".
Mr Alexander said: "Of course we want information sharing. The people who want to do harm to the UK operate internationally and those who are trying to keep us safe need to operate internationally as well.
"But on the other hand, in terms of the character and the nature and the timing of the requests that are made by the UK to the US, potentially involving UK citizens as well as international citizens, that needs to be conducted on the basis of the legal framework set out by Parliament."