Britain's enemies are "rubbing their hands with glee" over whistleblower Edward Snowden's NSA leaks, the MI6 chief said.
GCHQ have launched an online code breaking competition to find people capable of joining the Government's national cyber security teams.
The Foreign Secretary said British intelligence would never use its partnership with the United States to get around UK laws.
White House spokesman Jay Carney said US surveillance agencies were only interested in collecting data on people considered a threat to the United States.
Mr Carney told a regular White House news conference:
To the extent data is collected by the NSA [National Security Agency] through whatever means, we are not interested in the communications of people who are not valid foreign intelligence targets, and we are not after the information of ordinary Americans.
British intelligence agency GCHQ "would not confirm of deny the existence of the Squeaky Dolphin" monitoring programme, according to NBC News.
A spokesperson for the agency said GCHQ's work was "carried out in accordance with a strict legal and policy framework”.
This "ensure[s] that our activities are authorised, necessary and proportionate, and that there is rigorous oversight, including from the Secretary of State, the Interception and Intelligence Services Commissioners and the Parliamentary Intelligence and Security Committee", the spokesperson added.
The "Squeaky Dolphin" monitoring programme said to have been utilised by British intelligence agencies was not intended to spy on individuals, but it could be done, cyber-security experts told NBC News.
The experts claimed the documents released by Edward Snowden show GCHQ had to have been either physically able to tap the cables carrying the world’s internet traffic or able to use a third party to gain physical access to the massive stream of data.
Once the information has been gathered, intelligence agencies have the ability to extract some user information as well, they added.
US and British intelligence agencies have plotted ways to gather data from Angry Birds and other smartphone apps that "leak" users' personal information onto global networks, the Guardian reported, citing documents obtained from whistleblower Edward Snowden.
The US National Security Agency (NSA) and its British counterpart, the Government Communications Headquarters (GCHQ), had tried to exploit "leaky" smartphone apps that could disclose users' locations, age, gender and other personal information, according to the newspaper.
British intelligence agencies have the capacity to monitor social media sites such as Facebook and YouTube by tapping into the cables carrying the world's internet traffic, according to documents obtained by NBC News.
The documents, reportedly taken from the US National Security Agency by whistleblower Edward Snowden, show British spies demonstrated a pilot programme to their US counterparts in 2012.
The programme, called "Squeaky Dolphin", was able to monitor YouTube in real time, collect addresses and some other user information.
According to the “Psychology A New Kind of SIGDEV [Signals Development] presentation, the Government was also able to take part in “broad real-time monitoring of online activity” of URLs “liked” on Facebook, Blogspot/Blogger visits and Twitter.
Foreign Secretary William Hague has insisted that he has seen no evidence of breaches in the UK's protection of individuals' communications, following reports that British spies are able to look at texts.
The allegations, resulting from the latest leaks by whistleblower Edward Snowden, suggest a secret database created by the US National Security Agency collects nearly 200 million texts every day from around the world.
Hague refused to comment directly on the fresh claims, but told BBC Radio 4's Today programme: "I'm not going to comment on the detail of any allegations or leaks or alleged leaks. I can't possibly do that.
"But I can say what I said on June 10 to Parliament about our legal system, about the very strong system of checks and balances, of warrants being required from me or the Home Secretary to intercept the content of the communications of anyone within the United Kingdom."
The Foreign Secretary insisted he had not seen any evidence to suggest the evidence was breached, and claimed that the UK has one of the strongest systems in the world.
The Prime Minister and US President Barack Obama have discussed intelligence-gathering techniques in a phone conversation this afternoon.
– Number 10 spokesperson
Finally, the President updated the Prime Minister on the US signals intelligence review ahead of setting out tomorrow his Administration’s response to the review.
The two leaders welcomed the unique intelligence sharing relationship between their two countries.
The two leaders also discussed the progress made in destroying the Syrian government's chemical weapons stockpile and the need for a political solution to the conflict.
Nick Pickles, director of Big Brother Watch, which campaigns on privacy, civil liberties and levels of surveillance, said GCHQ "has serious questions to answer" after reports claimed that British spies could snoop on hundreds of millions of text messages.
– Nick Pickles, director of Big Brother Watch which campaigns on privacy
If an interception warrant for an individual is not in place, it is illegal to look at the content of a message.
Descriptions of content derived metadata suggest the content of texts is being collected and inspected in bulk and if this is the case GCHQ has serious questions to answer about whether it is operating under a perverse interpretation of the law cooked up in secret.
The telecoms companies providing our mobile phone services need to urgently reassure their customers that they are not handing over our data in bulk to the UK or US governments.
America's National Security Agency has stated that Dishfire - a secret operation which has reportedly collected millions of text messages that can be viewed by British spies - does exist and that it lawfully collects SMS data.
The NSA also said that privacy protections are in place for US citizens, according to Channel 4 News.
Meanwhile, GCHQ said: "All of GCHQ's work is carried out in accordance with the strict legal and policy framework which ensures that our activities are authorised, necessary and proportionate and that there is rigorous oversight."
Former Interception Commissioner Sir Swinton Thomas said reports that British spies have access to millions of text messages were "a worry" and that he would have been concerned about this kind of use of foreign intelligence agency data.
– Former Interception Commissioner Sir Swinton Thomas
Certainly in my time I would take the view that it not open to our intelligence services to obtain or certainly to use communications or data which would not have been lawful in this country.
It's not dissimilar to the question of whether you use material which you may have reason to believe has been obtained by torture.
It's a different area of course, but the concept is very similar.