The Foreign Secretary said British intelligence would never use its partnership with the United States to get around UK laws.
GCHQ (Government Communications Headquarters) is one of three UK intelligence agencies that form the UK's security and intelligence system.
Facebook, Google and Microsoft have all denied claims that they cooperated with US intelligence agencies to gather data on foreign users.
Prime Minister David Cameron stressed UK intelligence agencies operated within the law and were subject to "proper scrutiny" by politicians.
Speaking to ITV News Political Correspondent Libby Wiener Mr Cameron said the UK's intelligence services were necessary to protect citizens in a "dangerous world".
David Cameron's spokesman said the Prime Minister believes GCHQ operates within UK law, and that it was "fanciful" to think the agency would be trying to work out how to circumvent its legal framework. Speaking to reporters he said:
I think the PM's view is that the agencies operate within this framework and as the Foreign Secretary said the idea that in GCHQ people are sitting working out how to circumvent a UK law with another agency in another country is fanciful.
He thinks that the necessary and important frameworks are in place and that there has been a lot of questions that have been raised and the right thing to do is for the Foreign Secretary to go to the House and give a statement.
Tory Sir Malcolm Rifkind, chairman of the committee of MPs and peers which overseas the work of security services said GCHQ would need authority for any request to monitor emails of a UK citizen, even if it was carried out by US agencies. Speaking to BBC Radio 4's Today programme, he said:
One of the big questions that's being asked is if British intelligence agencies want to seek to know the content of emails, can they get round the normal law in the UK by simply asking an American agency to provide that information?
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.
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.
William Hague will face questions from MPs today over GCHQ's links to a controversial US internet monitoring programme.
The Foreign Secretary is due to make a statement to the Commons amid mounting pressure to reveal information about connections to the Prism system.
Speaking on the BBC's Andrew Marr Show yesterday, Mr Hague insisted the British eavesdropping agency had not been trying to dodge tough legal checks on their activities.
The law-abiding British public had "nothing to fear" from their work, he added.
Mr Hague said: "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.
Business Secretary Vince Cable said today that it was a possibility that the Prism system may have allowed the Government to operate a covert sort of snoopers' charter, after the Foreign Secretary claimed that GCHQ did not try to dodge tough legal checks on their activities.
Mr Cable told Sky News' Murnaghan programme: "One is that the Americans have developed this very sophisticated Prism system, which enables them to get access to data in other countries, with or without our knowledge.
"And there is a separate issue about whether GCHQ were involved in some collaborative exercise.
"I think a lot of people will be reassured that we do work well with the Americans, but the whole point about surveillance is you have got to have it when you're dealing with terrorism or other crimes".
Responding to William Hague's pledge to make a statement to parliament on GCHQ surveillance claims, shadow foreign secretary Douglas Alexander said:
I've said that it's right that we fully support our intelligence agencies in the work they do to keep us safe, while recognising that they must always operate within a framework of legality and accountability.
I will be asking the Foreign Secretary in the House of Commons tomorrow to clarify the role of his Department in overseeing those legal frameworks.
– Douglas Alexander MP, Shadow Foreign Secretary
William Hague must also inform the House of what steps he will take to support the work of the Intelligence and Security Committee as it looks in to these matters.
It is vital that the Government now reassures people who are rightly concerned about these reports.
William Hague told the BBC's Andrew Marr Show that normal British citizens have "nothing to fear" about the way GCHQ collects and monitors data.
"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," 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."
William Hague said he would not be able to comment on the exact nature of the data sharing an monitoring between US and British intelligence agencies.
But he insisted that the gathering of such intelligence is "governed by a very strong legal framework so that we get the balance right between the liberties and privacy of people and the security of the country."
"It provides for intelligence gathering that is authorised, necessary, proportionate and targeted," he said.
William Hague will give a statement to parliament tomorrow on the allegations surrounding GCHQ and its use of American web monitoring services, the Foreign Secretary told the BBC's Andrew Marr Show.