The Guardian via Getty Images HONG KONG - 2013: In this handout photo provided by The Guardian, Edward Snowden speaks during an interview in Hong Kong. Snowden, a 29-year-old former technical assistant for the CIA, revealed details of top-secret surveillance conducted by the United States' National Security Agency regarding telecom data.

More than two months after documents leaked by former contractor Edward Snowden first began appearing in the news media, the National Security Agency still doesn’t know the full extent of what he took, according to intelligence community sources, and is “overwhelmed” trying to assess the damage.

Officials, including NSA Director Keith Alexander, have assured the public that the government knows the scope of the damage, but two separate sources briefed on the matter told NBC News that the NSA has been unable to determine how many documents he took and what they are.

Sources said authorities believe the trove of unreleased materials includes details of data collection by U.S. allies, including the U.K., Canada, Australia and New Zealand. These English-speaking allies, known along with the U.S. as the "Five Eyes," are critical to U.S. intelligence efforts.

Snowden was working for Booz Allen Hamilton in Hawaii as a contractor for the NSA before he flew to Hong Kong in May 2013. Documents that he had leaked then became the basis of a series of articles by Guardian journalist Glenn Greenwald and Barton Gellman of the Washington Post about the extent of the NSA’s monitoring of electronic communications. Greenwald has told reporters that Snowden has leaked him and Laura Poitras, a documentary filmmaker, thousands of documents -- all of which have since been encrypted -- and that the encoded files have been shared with others

NSA had poor data compartmentalization, said the sources, allowing Snowden, who was a system administrator, to roam freely across wide areas. By using a “thin client” computer he remotely accessed the NSA data from his base in Hawaii.

One U.S. intelligence official said government officials “are overwhelmed" trying to account for what Snowden took. Another said that the NSA has a poor audit capability, which is frustrating efforts to complete a damage assessment.

Appearing at the Aspen Security Forum on July 18, NSA Director Alexander responded "Yes" when NBC News correspondent Pete Williams asked, "Do you feel you now know what (Snowden) got?" Asked "Was it a lot?", Alexander again said, "Yes."

On Tuesday, NSA spokesperson Vanee Vines said Alexander's Aspen answer was not intended as "a hard, 'We know everything, completely,' answer to Williams' question."

"He did not say the assessment had been completed in absolute terms," Vines added in an email. "The Director answered a question about his general sense."

The news comes two days after British authorities detained and questioned Greenwald’s partner, David Miranda, for nine hours at Heathrow airport outside London. On Sunday, Miranda was reportedly carrying a thumb drive of Snowden-related material from Berlin to Rio de Janeiro, where he and Greenwald live, when he was detained. British authorities kept the drive and his other computer hardware, according to published reports.

Miranda now says he plans to file a legal action against British authorities on Wednesday.

The U.S. charged Snowden with the theft of classified documents and violations of the Espionage Act. He is currently living in Russia, where he has been granted temporary asylum.

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