The agency is able to tap into and store data from the cables for up to 30 days so it can be analysed under an operation codenamed Tempora, reports claimed.
The Cheltenham-based agency would not comment on intelligence matters but insisted it was “scrupulous” in complying with the law.
The information is the latest leak from Mr Snowden, the National Security Agency (NSA) informer responsible for a string of disclosures about US intelligence operations.
Reports said there were two principal components to the agency’s surveillance programme, called Mastering the Internet and Global Telecoms Exploitation. It claimed the data was shared with, the NSA, the organisation’s US counterpart.
Meanwhile, a private plane is on standby to transport Snowden from Hong Kong to Iceland, an Icelandic businessman has revealed. Mr Snowden fled the US for Hong Kong after deciding to reveal the NSA’s secrets.
Olafur Vignir Sigurvinsson, who has connections to the WikiLeaks secret-spilling organisation, said he has access to planes in Hong Kong and mainland China that Mr Snowden could use. The businessman said he has not spoken directly with Mr Snowden but is in touch with a third party representing him.
But Iceland says it has received no asylum request from Mr Snowden, who has revealed his role in providing secret NSA documents about widespread surveillance programmes.
He said his group hopes to obtain Icelandic citizenship for Snowden. “We are hoping that the government does what they did with Bobby Fischer,” he said, referring to the late chessmaster who went to Iceland to escape US prosecution for breaking sanctions.