Critics said the revelations - made in 2012 documents obtained by US whistleblower Edward Snowden - showed much more oversight was needed over the Communications Security Establishment, or CSE.
The documents are the first indication from the Snowden files to show Canada has launched its own massive, globe-spanning Internet surveillance in a bid to counter extremists.
The covert dragnet, nicknamed Levitation, has covered allied countries and trading partners such as the United States, Britain, Brazil, Germany, Spain and Portugal, the report by CBC News and journalist Glenn Greenwald said.
CBC said the CSE nets what it said the agency calls 350 "interesting download events" each month.
CSE is a secretive body, which like the US National Security Agency, or NSA, monitors electronic communication and helps protect national computer networks. It is not allowed to target Canadians or Canadian corporations.
In the past, CSE has faced allegations that it has improperly intercepted Canadians' phone conversations and e-mails. CSE says it has safeguards in place to protect any information about Canadians it might inadvertently collect.
An independent watchdog monitors CSE, but the watchdog's powers are limited. Opposition parties moved in Parliament last October to give it a more robust role but were defeated by the governing Conservatives.
"We need to make sure there is proper public oversight of our national security agencies ... we have very serious concerns about how this government is keeping Canadians safe," said Justin Trudeau, leader of the opposition Liberal Party.
The Liberals lead most polls ahead of an October 2015 election.
Among CSE's hauls, the eavesdropping program has discovered a German hostage video and an uploaded document that revealed the hostage strategy of an al-Qaeda wing in North Africa, the CBC said.
The agency did not confirm the report, saying in a statement that "CSE's foreign signals intelligence has played a vital role in uncovering foreign-based extremists' efforts to attract, radicalise, and train individuals to carry out attacks".
The Snowden documents show the agency has sifted through 10 million to 15 million uploads a day of videos, music documents and other files hosted by 102 file-sharing websites.
Canada is part of the Five Eyes intelligence-sharing network, along with the United States, Britain, Australia and New Zealand.
In 2013, Brazilian President Dilma Rousseff demanded an explanation from Canada after a media report, also based on Snowden documents, said CSE spied on the South American country's mines and energy ministry.
Wesley Wark, one of Canada's top security experts, said Levitation might well be covered by CSE's foreign intelligence mandate, but questioned its effectiveness.
"Does this massive trawling of free download sites aimed at detecting terrorist communications or identities really deliver useful intelligence?" asked Wark, a University of Ottawa professor, noting CSE had talked of only two successes.
In November 2013, the CBC cited other Snowden documents that it said showed Canada had allowed the NSA to conduct widespread surveillance during the 2010 Group of 20 summit in Toronto.
Last August, the government watchdog said CSE should tighten its procedures for handling the private calls and e-mails it intercepts. — Reuters
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